<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/0ea882e0-1852-4606-b90a-e77f5f4384fd/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls6 ws0"><span class="fc1 sc0">E</span><span class="fc1 sc0">j</span><span class="fc1 sc0">e</span><span class="fc1 sc0">r</span><span class="fc1 sc0">ci</span><span class="blank _0"></span><span class="fc1 sc0">ci</span><span class="fc1 sc0">o</span><span class="fc1 sc0">s</span><span class="blank"> </span><span class="fc1 sc0">d</span><span class="fc1 sc0">e</span><span class="blank"> </span><span class="fc1 sc0">pr</span><span class="blank _0"></span><span class="fc1 sc0">o</span><span class="blank _0"></span><span class="fc1 sc0">gr</span><span class="blank _0"></span><span class="fc1 sc0">e</span><span class="fc1 sc0">si</span><span class="fc1 sc0">one</span><span class="fc1 sc0">s</span></div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls6 ws1">1.<span class="blank _1"> </span>Determinar<span class="blank"> </span>si<span class="blank"> </span>las<span class="blank"> </span>siguientes<span class="blank"> </span>progr<span class="blank _0"></span>esiones<span class="blank"> </span>son<span class="blank"> </span>o<span class="blank"> </span>no<span class="blank"> </span>son<span class="blank"> </span>aritméticas.<span class="blank _2"> </span>En<span class="blank"> </span>caso<span class="blank"> </span>a\ue7fdr<span class="blank _0"></span>-</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls6 ws2">mativo<span class="blank _0"></span>,<span class="blank"> </span>calcular<span class="blank"> </span>la<span class="blank"> </span>diferencia<span class="blank"> </span>de<span class="blank"> </span>cada<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión.</div><div class="t m0 x4 h3 y4 ff2 fs1 fc0 sc0 ls6 ws2">(a)<span class="blank _1"> </span>1,<span class="blank"> </span>4,<span class="blank"> </span>7,<span class="blank"> </span>10,<span class="blank"> </span>13,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x5 h3 y5 ff2 fs1 fc0 sc0 ls6 ws2">(b)<span class="blank _1"> </span>1,<span class="blank"> </span>0,<span class="blank"> </span>1,<span class="blank"> </span>0,<span class="blank"> </span>1,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x4 h3 y6 ff2 fs1 fc0 sc0 ls6 ws2">(c)<span class="blank _1"> </span>1,<span class="blank"> </span>0,<span class="blank"> </span><span class="ff3 ws3">\u2212</span><span class="ws4">1,<span class="blank"> </span><span class="ff3 ls0">\u2212</span><span class="ws5">2,<span class="blank"> </span><span class="ff3 ls0">\u2212</span>3,<span class="blank"> </span><span class="ff3">\u2026</span></span></span></div><div class="t m0 x5 h3 y7 ff2 fs1 fc0 sc0 ls6 ws2">(d)<span class="blank _1"> </span>1,<span class="blank"> </span>3,<span class="blank"> </span>6,<span class="blank"> </span>10,<span class="blank"> </span>15,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x5 h3 y8 ff2 fs1 fc0 sc0 ls6 ws2">(e)<span class="blank _1"> </span>1,<span class="blank"> </span>2,<span class="blank"> </span>3,<span class="blank"> </span>4,<span class="blank"> </span>5,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x2 h3 y9 ff2 fs1 fc0 sc0 ls6 ws6">2.<span class="blank _1"> </span>Calcular<span class="blank"> </span>los<span class="blank"> </span>5<span class="blank"> </span>primer<span class="blank _0"></span>os<span class="blank"> </span>términos<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>pr<span class="blank _0"></span>ogresión<span class="blank"> </span>aritmética<span class="blank"> </span>cuyo<span class="blank"> </span>término<span class="blank"> </span>gener<span class="blank _0"></span>al</div><div class="t m0 x3 h3 ya ff2 fs1 fc0 sc0 ls6">es</div><div class="t m0 x6 h4 yb ff3 fs1 fc0 sc0 ls1">\ud835\udc4e<span class="fs2 ls2 v1">\ud835\udc5b</span><span class="ls6 ws7">=<span class="blank _3"> </span>\u22122\ud835\udc5b<span class="blank _3"> </span>\u2212<span class="blank"> </span>1</span></div><div class="t m0 x2 h3 yc ff2 fs1 fc0 sc0 ls6 ws2">3.<span class="blank _1"> </span>El<span class="blank"> </span>término<span class="blank"> </span>general<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es</div><div class="t m0 x7 h4 yd ff3 fs1 fc0 sc0 ls1">\ud835\udc4e<span class="fs2 ls3 v1">\ud835\udc5b</span><span class="ls6 ws7">=<span class="blank _3"> </span>3\ud835\udc5b<span class="blank _3"> </span>+<span class="blank"> </span>2</span></div><div class="t m0 x3 h3 ye ff2 fs1 fc0 sc0 ls6 ws2">¿Cuál<span class="blank"> </span>es<span class="blank"> </span>el<span class="blank"> </span>primer<span class="blank"> </span>término<span class="blank"> </span>y<span class="blank"> </span>la<span class="blank"> </span>diferencia<span class="blank"> </span>de<span class="blank"> </span>esa<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión?</div><div class="t m0 x2 h3 yf ff2 fs1 fc0 sc0 ls6 ws2">4.<span class="blank _1"> </span>El<span class="blank"> </span>término<span class="blank"> </span>general<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es</div><div class="t m0 x6 h4 y10 ff3 fs1 fc0 sc0 ls1">\ud835\udc4e<span class="fs2 ls3 v1">\ud835\udc5b</span><span class="ls6 ws7">=<span class="blank _3"> </span>3(\ud835\udc5b<span class="blank _3"> </span>\u2212<span class="blank"> </span>1)</span></div><div class="t m0 x3 h3 y11 ff2 fs1 fc0 sc0 ls6 ws2">¿Cuál<span class="blank"> </span>es<span class="blank"> </span>el<span class="blank"> </span>primer<span class="blank"> </span>término<span class="blank"> </span>y<span class="blank"> </span>la<span class="blank"> </span>diferencia<span class="blank"> </span>de<span class="blank"> </span>esa<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión?</div><div class="t m0 x2 h3 y12 ff2 fs1 fc0 sc0 ls6 ws2">5.<span class="blank _1"> </span>El<span class="blank"> </span>término<span class="blank"> </span>general<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es</div><div class="t m0 x8 h4 y13 ff3 fs1 fc0 sc0 ls6 ws3">\ud835\udc4e<span class="fs2 ls2 v1">\ud835\udc5b</span><span class="ws8">=<span class="blank _3"> </span>10<span class="blank"> </span>\u2212<span class="blank"> </span>10\ud835\udc5b</span></div><div class="t m0 x3 h3 y14 ff2 fs1 fc0 sc0 ls6 ws2">¿Cuál<span class="blank"> </span>es<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>sus<span class="blank"> </span>10<span class="blank"> </span>primeros<span class="blank"> </span>términos?</div><div class="t m0 x2 h3 y15 ff2 fs1 fc0 sc0 ls6 ws9">6.<span class="blank _1"> </span>Calcular<span class="blank"> </span>la<span class="blank"> </span>difer<span class="blank _0"></span>encia<span class="blank"> </span>y<span class="blank"> </span>el<span class="blank"> </span>término<span class="blank"> </span>gener<span class="blank _0"></span>al<span class="blank"> </span>de<span class="blank"> </span>las<span class="blank"> </span>siguientes<span class="blank"> </span>progr<span class="blank _0"></span>esiones<span class="blank"> </span>aritméti-</div><div class="t m0 x3 h3 y16 ff2 fs1 fc0 sc0 ls6">cas:</div><div class="t m0 x4 h3 y17 ff2 fs1 fc0 sc0 ls6 ws2">(a)<span class="blank _1"> </span>11,<span class="blank"> </span>22,<span class="blank"> </span>33,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x5 h3 y18 ff2 fs1 fc0 sc0 ls6 ws2">(b)<span class="blank _1"> </span>35,<span class="blank"> </span>42,<span class="blank"> </span>49,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x2 h3 y19 ff2 fs1 fc0 sc0 ls6 ws2">7.<span class="blank _1"> </span>Calcular<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>5<span class="blank"> </span>primer<span class="blank _0"></span>os<span class="blank"> </span>términos<span class="blank"> </span>de<span class="blank"> </span>las<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esiones:</div><div class="t m0 x4 h3 y1a ff2 fs1 fc0 sc0 ls6 ws2">(a)<span class="blank _1"> </span>5,<span class="blank"> </span>8,<span class="blank"> </span>11,<span class="blank"> </span>14,<span class="blank"> </span><span class="ff3 v0">\u2026</span></div><div class="t m0 x5 h3 y1b ff2 fs1 fc0 sc0 ls6 ws2">(b)<span class="blank _1"> </span>13,<span class="blank"> </span>16,<span class="blank"> </span>19,<span class="blank"> </span><span class="ff3">\u2026</span></div><div class="t m0 x2 h3 y1c ff2 fs1 fc0 sc0 ls6 wsa">8.<span class="blank _1"> </span>Marta<span class="blank"> </span>tiene<span class="blank"> </span>un<span class="blank"> </span>armario<span class="blank"> </span>con<span class="blank"> </span>10<span class="blank"> </span>cajones<span class="blank"> </span>numer<span class="blank _0"></span>ados<span class="blank"> </span>del<span class="blank"> </span>1<span class="blank"> </span>al<span class="blank"> </span>10<span class="blank"> </span>y<span class="blank"> </span>guarda<span class="blank"> </span><span class="ff3 ls4">\ud835\udc5b</span>objetos</div><div class="t m0 x3 h3 y1d ff2 fs1 fc0 sc0 ls6 wsb">en<span class="blank"> </span>el<span class="blank"> </span>cajón<span class="blank"> </span>número<span class="blank"> </span><span class="ff3 ls5">\ud835\udc5b</span>.<span class="blank _4"> </span>Después<span class="blank"> </span>de<span class="blank"> </span>haber<span class="blank"> </span>usado<span class="blank"> </span>los<span class="blank"> </span>10<span class="blank"> </span>cajones,<span class="blank"> </span>¿cuántos<span class="blank"> </span>objetos</div><div class="t m0 x3 h3 y1e ff2 fs1 fc0 sc0 ls6 wsc">ha<span class="blank"> </span>guardado<span class="blank"> </span>Mar<span class="blank _0"></span>ta<span class="blank"> </span>en<span class="blank"> </span>total?</div><div class="t m0 x9 h3 y1f ff2 fs1 fc0 sc0 ls6"><span class="fc1 sc0">1</span></div><div class="t m0 xa h5 y20 ff4 fs3 fc0 sc0 ls6 wsd"><span class="fc1 sc0">1</span><span class="blank _5"></span><span class="ff5"><span class="fc1 sc0">1</span></span></div><div class="t m0 xb h6 y21 ff6 fs4 fc0 sc0 ls6 wse"><span class="fc1 sc0">Progresiones </span><span class="fc1 sc0">aritméticas</span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x1 y22 w2 h7" alt="" src="https://files.passeidireto.com/0ea882e0-1852-4606-b90a-e77f5f4384fd/bg2.png"><div class="t m0 x2 h3 y23 ff2 fs1 fc0 sc0 ls6 wsf">9.<span class="blank _1"> </span>El<span class="blank"> </span>sexto<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>pr<span class="blank _0"></span>ogresión<span class="blank"> </span>aritmética<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 ls7 v1">6</span><span class="ls6 ws10">=<span class="blank"> </span>36<span class="blank"> </span></span></span>y<span class="blank"> </span>el<span class="blank"> </span>séptimo<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 ls7 v1">7</span><span class="ls6 ws10">=<span class="blank"> </span>42</span></span><span class="ws11">.<span class="blank"> </span>¿Cuál</span></div><div class="t m0 x3 h3 y24 ff2 fs1 fc0 sc0 ls6 ws2">es<span class="blank"> </span>el<span class="blank"> </span>primer<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>progr<span class="blank _0"></span>esión?<span class="blank _6"> </span>¿Y<span class="blank"> </span>la<span class="blank"> </span>diferencia?</div><div class="t m0 xc h3 y25 ff2 fs1 fc0 sc0 ls6 ws12">10.<span class="blank _1"> </span>El<span class="blank"> </span>tercer<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>pr<span class="blank _0"></span>ogr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ws3">\ud835\udc4e<span class="fs2 ls8 v1">3</span><span class="ws13">=<span class="blank"> </span>14<span class="blank _3"> </span></span></span>y<span class="blank"> </span>el<span class="blank"> </span>quinto<span class="blank _7"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 ls8 v1">5</span><span class="ls6 ws13">=<span class="blank"> </span>20</span></span><span class="ws14">.<span class="blank"> </span>¿Cuál</span></div><div class="t m0 x3 h3 y26 ff2 fs1 fc0 sc0 ls6 ws2">es<span class="blank"> </span>el<span class="blank"> </span>primer<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>progr<span class="blank _0"></span>esión?<span class="blank _6"> </span>¿Y<span class="blank"> </span>la<span class="blank"> </span>diferencia?</div><div class="t m0 xc h3 y27 ff2 fs1 fc0 sc0 ls6 ws15">11.<span class="blank _1"> </span>El<span class="blank"> </span>quinto<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>progr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 ls9 v1">5</span><span class="ls6 ws16">=<span class="blank"> </span>45<span class="blank"> </span></span></span><span class="ws17">y<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>5<span class="blank"> </span>primer<span class="blank _0"></span>os</span></div><div class="t m0 x3 h3 y28 ff2 fs1 fc0 sc0 ls6 ws18">términos<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ws3">\ud835\udc46<span class="fs2 lsa v1">5</span><span class="ws19">=<span class="blank"> </span>115</span></span><span class="ws2">.<span class="blank _6"> </span>¿Cuál<span class="blank"> </span>es<span class="blank"> </span>el<span class="blank"> </span>primer<span class="blank"> </span>término?</span></div><div class="t m0 xc h3 y29 ff2 fs1 fc0 sc0 ls6 ws17">12.<span class="blank _1"> </span>El<span class="blank"> </span>primer<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>progr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsb v1">1</span><span class="ls6 ws1a">=<span class="blank"> </span>3<span class="blank"> </span></span></span>y<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>5<span class="blank"> </span>primer<span class="blank _0"></span>os</div><div class="t m0 x3 h3 y2a ff2 fs1 fc0 sc0 ls6 ws18">términos<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ws3">\ud835\udc46<span class="fs2 lsa v1">5</span><span class="ws19">=<span class="blank"> </span>25</span></span><span class="ws2">.<span class="blank _6"> </span>¿Cuál<span class="blank"> </span>es<span class="blank"> </span>el<span class="blank"> </span>quinto<span class="blank"> </span>término?</span></div><div class="t m0 xc h3 y2b ff2 fs1 fc0 sc0 ls6 ws1b">13.<span class="blank _1"> </span>El<span class="blank"> </span>quinto<span class="blank"> </span>término<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>progr<span class="blank _0"></span>esión<span class="blank"> </span>aritmética<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsc v1">5</span><span class="ls6 ws1c">=<span class="blank"> </span>0<span class="blank _7"> </span></span></span><span class="ws1d">y<span class="blank"> </span>su<span class="blank"> </span>difer<span class="blank _0"></span>encia<span class="blank"> </span>es<span class="blank"> </span><span class="ff3 ws1e">\ud835\udc51<span class="blank _6"> </span>=<span class="blank"> </span>\u22123</span>.</span></div><div class="t m0 x3 h3 y2c ff2 fs1 fc0 sc0 ls6 ws2">¿Cuál<span class="blank"> </span>es<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>5<span class="blank"> </span>primeros<span class="blank"> </span>términos<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>sucesión?</div><div class="t m0 xc h3 y2d ff2 fs1 fc0 sc0 ls6 ws2">14.<span class="blank _1"> </span>Calcula<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>todos<span class="blank"> </span>los<span class="blank"> </span>númer<span class="blank _0"></span>os<span class="blank"> </span>par<span class="blank _0"></span>es<span class="blank"> </span>entr<span class="blank _0"></span>e<span class="blank"> </span>1<span class="blank"> </span>y<span class="blank"> </span>1000.</div><div class="t m0 xc h3 y2e ff2 fs1 fc0 sc0 ls6 ws2">15.<span class="blank _1"> </span>Calcula<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>todos<span class="blank"> </span>los<span class="blank"> </span>númer<span class="blank _0"></span>os<span class="blank"> </span>impar<span class="blank _0"></span>es<span class="blank"> </span>entr<span class="blank _0"></span>e<span class="blank"> </span>1<span class="blank"> </span>y<span class="blank"> </span>1000.</div><div class="t m0 x1 h8 y2f ff2 fs0 fc0 sc0 ls6">Soluciones</div><div class="t m0 x2 h3 y30 ff2 fs1 fc0 sc0 ls6 ws1d">1.<span class="blank _1"> </span>(a)<span class="blank"> </span>Sí<span class="blank"> </span>es<span class="blank"> </span>aritmética.<span class="blank _8"> </span><span class="ff3 ws1c">\ud835\udc51<span class="blank _6"> </span>=<span class="blank"> </span>3</span>.<span class="blank _8"> </span>(b)<span class="blank"> </span>No<span class="blank"> </span>es<span class="blank"> </span>aritmética.<span class="blank _8"> </span>(c)<span class="blank"> </span>Es<span class="blank"> </span>aritmética.<span class="blank _8"> </span><span class="ff3 ws1c">\ud835\udc51<span class="blank _6"> </span>=<span class="blank"> </span>\u22121</span>.<span class="blank _8"> </span>(d)<span class="blank"> </span>No<span class="blank"> </span>es</div><div class="t m0 x3 h3 y31 ff2 fs1 fc0 sc0 ls6 ws2">aritmética.<span class="blank _6"> </span>(e)<span class="blank"> </span>Es<span class="blank"> </span>aritmética.<span class="blank _4"> </span><span class="ff3 ws19">\ud835\udc51<span class="blank _6"> </span>=<span class="blank"> </span>1</span>.</div><div class="t m0 x2 h3 y32 ff2 fs1 fc0 sc0 ls6 ws1f">2.<span class="blank"> </span><span class="ff3 ls0">\u2212</span><span class="ws5">3,<span class="blank"> </span><span class="ff3 ls0">\u2212</span>5,<span class="blank"> </span><span class="ff3 ls0">\u2212</span>7,<span class="blank"> </span><span class="ff3 ls0">\u2212</span>9,<span class="blank"> </span><span class="ff3 ls0">\u2212</span>11</span></div><div class="t m0 x2 h3 y33 ff2 fs1 fc0 sc0 ls6 ws1f">3.<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsa v1">1</span><span class="ls6 ws19">=<span class="blank"> </span>5</span></span><span class="lsd">,</span><span class="ff3 ws19">\ud835\udc51<span class="blank _9"> </span>=<span class="blank"> </span>3</span></div><div class="t m0 x2 h3 y34 ff2 fs1 fc0 sc0 ls6 ws1f">4.<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsa v1">1</span><span class="ls6 ws19">=<span class="blank"> </span>0</span></span><span class="lsd">,</span><span class="ff3 ws19">\ud835\udc51<span class="blank _9"> </span>=<span class="blank"> </span>3</span></div><div class="t m0 x2 h3 y35 ff2 fs1 fc0 sc0 ls6 ws1f">5.<span class="blank"> </span><span class="ff3 ws3">\ud835\udc46<span class="fs2 ws20 v1">10<span class="blank"> </span></span><span class="ws19">=<span class="blank"> </span>\u2212450</span></span></div><div class="t m0 x2 h3 y36 ff2 fs1 fc0 sc0 ls6 ws21">6.<span class="blank _1"> </span>(a)<span class="blank"> </span><span class="ff3 ws19">\ud835\udc51<span class="blank _9"> </span>=<span class="blank"> </span>11</span><span class="lse">,</span><span class="ff3 ws3">\ud835\udc4e<span class="fs2 ls2 v1">\ud835\udc5b</span><span class="ws22">=<span class="blank _3"> </span>11\ud835\udc5b<span class="blank"> </span></span></span><span class="ws23">.<span class="blank _6"> </span>(b)<span class="blank"> </span><span class="ff3 ws19">\ud835\udc51<span class="blank _9"> </span>=<span class="blank"> </span>3</span><span class="lse">,</span><span class="ff3 ws3">\ud835\udc4e<span class="fs2 ls2 v1">\ud835\udc5b</span><span class="ws7">=<span class="blank _3"> </span>3\ud835\udc5b<span class="blank _3"> </span>+<span class="blank"> </span>10</span></span></span></div><div class="t m0 x2 h3 y37 ff2 fs1 fc0 sc0 ls6 ws21">7.<span class="blank _1"> </span>(a)<span class="blank"> </span><span class="ff3 ws3">\ud835\udc46<span class="fs2 lsa v1">5</span><span class="ws19">=<span class="blank"> </span>55</span></span><span class="wsc">,<span class="blank"> </span>(b)<span class="blank"> </span><span class="ff3 ws3">\ud835\udc46<span class="fs2 lsf v1">5</span><span class="ws19">=<span class="blank"> </span>95</span></span></span></div><div class="t m0 x2 h3 y38 ff2 fs1 fc0 sc0 ls6 wsc">8.<span class="blank _1"> </span>55<span class="blank"> </span>objetos</div><div class="t m0 x2 h3 y39 ff2 fs1 fc0 sc0 ls6 ws1f">9.<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsa v1">1</span><span class="ls6 ws19">=<span class="blank"> </span>6</span></span><span class="lsd">,</span><span class="ff3 ws19">\ud835\udc51<span class="blank _9"> </span>=<span class="blank"> </span>6</span></div><div class="t m0 xc h3 y3a ff2 fs1 fc0 sc0 ls6 ws24">10.<span class="blank"> </span><span class="ff3 ws19">\ud835\udc51<span class="blank _9"> </span>=<span class="blank"> </span>3</span><span class="lsd">,<span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsf v1">1</span><span class="ls6 ws19">=<span class="blank"> </span>8</span></span></span></div><div class="t m0 xc h3 y3b ff2 fs1 fc0 sc0 ls6 ws24">11.<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsa v1">1</span><span class="ls6 ws19">=<span class="blank"> </span>1</span></span></div><div class="t m0 xc h3 y3c ff2 fs1 fc0 sc0 ls6 ws24">12.<span class="blank"> </span><span class="ff3 ls1">\ud835\udc4e<span class="fs2 lsa v1">5</span><span class="ls6 ws19">=<span class="blank"> </span>7</span></span></div><div class="t m0 xc h3 y3d ff2 fs1 fc0 sc0 ls6 ws24">13.<span class="blank"> </span><span class="ff3 ws3">\ud835\udc46<span class="fs2 lsa v1">5</span><span class="ws19">=<span class="blank"> </span>30</span></span></div><div class="t m0 xc h3 y3e ff2 fs1 fc0 sc0 ls6 ws24">14.<span class="blank"> </span><span class="ff3 ws19">\ud835\udc46<span class="blank _7"> </span>=<span class="blank"> </span>250500</span></div><div class="t m0 xc h3 y3f ff2 fs1 fc0 sc0 ls6 ws24">15.<span class="blank"> </span><span class="ff3 ws19">\ud835\udc46<span class="blank _7"> </span>=<span class="blank"> </span>250000</span></div><div class="t m0 x9 h3 y1f ff2 fs1 fc0 sc0 ls6"><span class="fc1 sc0">2</span></div><div class="t m0 xa h5 y20 ff4 fs3 fc0 sc0 ls6 wsd"><span class="fc1 sc0">2</span><span class="blank _5"></span><span class="ff5"><span class="fc1 sc0">2</span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w3 h9" data-page-no="3"><div class="pc pc3 w3 h9"><img fetchpriority="low" loading="lazy" class="bi x1 y40 w4 ha" alt="" src="https://files.passeidireto.com/0ea882e0-1852-4606-b90a-e77f5f4384fd/bg3.png"><div class="t m0 xd hb y41 ff7 fs0 fc0 sc0 ls6 ws25">Pr<span class="blank _0"></span>ogresiones<span class="blank"> </span>geom<span class="v2">´</span></div><div class="t m0 xe hc y41 ff7 fs0 fc0 sc0 ls6">etricas</div><div class="t m0 x2 hd y42 ff8 fs1 fc0 sc0 ls6 ws26">1.<span class="blank _1"> </span>De<span class="blank"> </span>las<span class="blank"> </span>siguien<span class="blank _0"></span>tes<span class="blank"> </span>progresiones,<span class="blank"> </span>¿cu´<span class="blank _a"></span>ales<span class="blank"> </span>son<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etricas?<span class="blank"> </span>Halla<span class="blank"> </span>la<span class="blank"> </span>raz´<span class="blank _a"></span>on<span class="blank"> </span>de<span class="blank"> </span>aqu´<span class="blank _b"></span>ellas</div><div class="t m0 x3 hd y43 ff8 fs1 fc0 sc0 ls6 ws27">que<span class="blank"> </span>lo<span class="blank"> </span>sean.</div><div class="t m0 xf hd y44 ff9 fs1 fc0 sc0 ls10">a<span class="ff8 ls6 ws28">)<span class="blank _1"> </span>80,<span class="blank"> </span>40,<span class="blank"> </span>20,<span class="blank"> </span>10,<span class="blank"> </span><span class="ffa ws29">.<span class="blank"> </span>.<span class="blank"> </span>.</span></span></div><div class="t m0 xf hd y45 ff9 fs1 fc0 sc0 ls11">b<span class="ff8 ls6 ws2a">)<span class="blank _1"> </span>64,<span class="blank"> </span><span class="ffb ws2b">\u2212</span><span class="ws27">16,<span class="blank"> </span>4,<span class="blank"> </span><span class="ffb ls12">\u2212</span><span class="ws2c">1,<span class="blank"> </span><span class="ffa ws29">.<span class="blank"> </span>.<span class="blank"> </span>.</span></span></span></span></div><div class="t m0 xf hd y46 ff9 fs1 fc0 sc0 ls13">c<span class="ff8 ls6 ws28">)<span class="blank _1"> </span>24,<span class="blank"> </span>20,<span class="blank"> </span>14,<span class="blank"> </span>10,<span class="blank"> </span><span class="ffa ws29">.<span class="blank"> </span>.<span class="blank"> </span>.</span></span></div><div class="t m0 x4 he y47 ff9 fs1 fc0 sc0 ls14">d<span class="ff8 ls15">)<span class="ffb ls16 v3">\u221a</span><span class="ls6 ws27">2,<span class="blank"> </span>2,<span class="blank"> </span>2<span class="ffb ls16 v3">\u221a</span>2,<span class="blank"> </span>4,<span class="blank"> </span>4<span class="ffb ls16 v3">\u221a</span><span class="ws2d">2,<span class="blank"> </span><span class="ffa ws29">.<span class="blank"> </span>.<span class="blank"> </span>.</span></span></span></span></div><div class="t m0 x2 hd y48 ff8 fs1 fc0 sc0 ls6 ws27">2.<span class="blank _1"> </span>Escribe<span class="blank"> </span>los<span class="blank"> </span>4<span class="blank"> </span>primeros<span class="blank"> </span>t´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>progresi´<span class="blank _a"></span>on<span class="blank"> </span>geom´<span class="blank _b"></span>etrica<span class="blank"> </span><span class="ffa ls17">a<span class="ffc fs5 ls18 v4">n</span></span><span class="ws2e">=<span class="blank _7"> </span>3<span class="blank"> </span><span class="ffb ls19">·</span><span class="ws2f">2<span class="ffc fs5 v5">n</span></span></span></div><div class="t m0 x2 hd y49 ff8 fs1 fc0 sc0 ls6 ws30">3.<span class="blank _1"> </span>En<span class="blank"> </span>una<span class="blank"> </span>progresi´<span class="blank _a"></span>on<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etrica<span class="blank"> </span>se<span class="blank"> </span>cono<span class="blank _c"> </span>ce<span class="blank"> </span><span class="ffa ws31">a<span class="ffd fs5 ls1a v4">1</span></span><span class="ws32">=<span class="blank"> </span>81<span class="blank _4"> </span>y<span class="blank _d"> </span><span class="ffa ls17">a<span class="ffd fs5 ls1b v4">2</span></span><span class="ws26">=<span class="blank _6"> </span>243.<span class="blank"> </span>Calcula<span class="blank"> </span>la<span class="blank"> </span>raz´<span class="blank _a"></span>on<span class="blank"> </span>y<span class="blank"> </span>el</span></span></div><div class="t m0 x3 hd y4a ff8 fs1 fc0 sc0 ls6 ws33">o<span class="blank"> </span>cta<span class="blank _0"></span>v<span class="blank _0"></span>o<span class="blank _9"> </span>t´<span class="blank _b"></span>ermino.</div><div class="t m0 x2 hd y4b ff8 fs1 fc0 sc0 ls6 ws34">4.<span class="blank _1"> </span>Hallar<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>indicados<span class="blank"> </span>en<span class="blank"> </span>las<span class="blank"> </span>progresiones<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etricas<span class="blank"> </span>que<span class="blank"> </span>se</div><div class="t m0 x3 hd y4c ff8 fs1 fc0 sc0 ls6 ws27">indican<span class="blank"> </span>a<span class="blank"> </span>con<span class="blank _0"></span>tin<span class="blank _0"></span>uaci´<span class="blank _a"></span>on:</div><div class="t m0 x10 hd y4d ff8 fs1 fc0 sc0 ls6 ws35">a)<span class="blank _e"> </span>4<span class="blank"> </span>+<span class="blank"> </span>8<span class="blank"> </span>+<span class="blank"> </span>16<span class="blank"> </span>+<span class="blank"> </span>32<span class="blank"> </span>+<span class="blank"> </span>64<span class="blank"> </span>+<span class="blank"> </span>128<span class="blank _e"> </span>6<span class="blank _6"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos</div><div class="t m0 x10 hf y4e ff8 fs1 fc0 sc0 ls6 ws35">b)<span class="blank _f"> </span>81<span class="blank"> </span>+<span class="blank"> </span>27<span class="blank"> </span>+<span class="blank"> </span>9<span class="blank"> </span>+<span class="blank"> </span>3<span class="blank"> </span>+<span class="blank"> </span>1<span class="blank"> </span>+<span class="blank _6"> </span><span class="v6">1</span></div><div class="t m0 x11 h10 y4f ff8 fs1 fc0 sc0 ls1c">3<span class="ls1d v6">+</span><span class="ls6 v7">1</span></div><div class="t m0 x12 h11 y4f ff8 fs1 fc0 sc0 ls1e">9<span class="ls6 ws27 v6">7<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos</span></div><div class="t m0 x10 h12 y50 ff8 fs1 fc0 sc0 ls6 ws36">c)<span class="blank"> </span><span class="v6">15</span></div><div class="t m0 x13 h10 y51 ff8 fs1 fc0 sc0 ls1f">8<span class="ls1d v6">+</span><span class="ls6 v7">3</span></div><div class="t m0 x14 h10 y51 ff8 fs1 fc0 sc0 ls1c">4<span class="ls20 v6">+</span><span class="ls6 v7">3</span></div><div class="t m0 x15 h13 y51 ff8 fs1 fc0 sc0 ls6 ws37">10<span class="blank"> </span><span class="ffb ws38 v6">·<span class="blank"> </span>·<span class="blank"> </span>·<span class="blank _10"> </span></span><span class="ws27 v6">4<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos</span></div><div class="t m0 x10 hd y52 ff8 fs1 fc0 sc0 ls6 ws39">d)<span class="blank"> </span>0<span class="ffa ls21">,</span><span class="ls22 ws3a">5+0<span class="blank _11"></span><span class="ffa ls6 ws31">,<span class="ff8 ls22 ws3a">3+0<span class="blank _11"></span><span class="ffa ls21">,<span class="ff8 ls6 ws3b">18<span class="blank"> </span><span class="ffa ws29">.<span class="blank"> </span>.<span class="blank"> </span>.<span class="blank _12"> </span></span><span class="ws27">5<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos</span></span></span></span></span></span></div><div class="t m0 x10 hd y53 ff8 fs1 fc0 sc0 ls6 ws3c">e)<span class="blank"> </span>1<span class="ffa ls23">,<span class="ffb ls12">\u2212</span></span><span class="ws2f">1<span class="ffa ls23">,</span>1<span class="ffa ls23">,</span><span class="ffb ws2b">\u2212</span>1<span class="ffa ls24">,</span>1<span class="ffa ls23">,</span><span class="ffb ws2b">\u2212</span><span class="ls25">1</span><span class="ffa ws29">.<span class="blank"> </span>.<span class="blank"> </span>.<span class="blank _13"> </span></span><span class="ws27">10<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos</span></span></div><div class="t m0 x2 h14 y54 ff8 fs1 fc0 sc0 ls6 ws3d">5.<span class="blank _1"> </span>Calcular<span class="blank"> </span>el<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>ermino<span class="blank"> </span>6<span class="ffd fs5 ls26 v5">o</span>y<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>progresi´<span class="blank _a"></span>on<span class="blank"> </span>geom´<span class="blank _b"></span>etrica,<span class="blank"> </span>sa-</div><div class="t m0 x3 h15 y55 ff8 fs1 fc0 sc0 ls6 ws27">biendo<span class="blank"> </span>que<span class="blank"> </span><span class="ffa ls17">a<span class="ffd fs5 ls27 v4">1</span></span><span class="ws3e">=<span class="blank"> </span>4,<span class="blank _6"> </span><span class="ffa ls28">r</span><span class="ls29">=</span><span class="ffd fs5 v8">1</span></span></div><div class="t m0 x16 h16 y56 ffd fs5 fc0 sc0 ls2a">2<span class="ff8 fs1 ls6 ws27 v5">,<span class="blank"> </span>y<span class="blank"> </span>ha<span class="blank _0"></span>y<span class="blank"> </span>que<span class="blank"> </span>sumar<span class="blank"> </span>hasta<span class="blank"> </span>el<span class="blank"> </span>6<span class="ffd fs5 ls2b v5">o</span><span class="ws2f">t<span class="blank _0"></span>´<span class="blank _b"></span>ermino.</span></span></div><div class="t m0 x2 hd y57 ff8 fs1 fc0 sc0 ls6 ws27">6.<span class="blank _1"> </span>Hallar<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>las<span class="blank"> </span>progresiones<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etricas<span class="blank"> </span>in\ufb01nitas:</div><div class="t m0 x17 hf y58 ff8 fs1 fc0 sc0 ls6 ws35">a)<span class="blank _14"> </span>8<span class="blank"> </span>+<span class="blank"> </span>4<span class="blank"> </span>+<span class="blank"> </span>2<span class="blank"> </span>+<span class="blank"> </span>1<span class="blank"> </span>+<span class="blank _6"> </span><span class="v6">1</span></div><div class="t m0 x18 h10 y59 ff8 fs1 fc0 sc0 ls1c">2<span class="ls1d v6">+</span><span class="ls6 v7">1</span></div><div class="t m0 x19 h11 y59 ff8 fs1 fc0 sc0 ls1c">4<span class="ls2c v6">+<span class="ffb ls6 ws38">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x17 hf y5a ff8 fs1 fc0 sc0 ls6 ws3f">b)<span class="blank _15"> </span>1<span class="blank"> </span><span class="ffb ls2d">\u2212</span><span class="v6">1</span></div><div class="t m0 x1a h10 y5b ff8 fs1 fc0 sc0 ls1c">2<span class="ls1d v6">+</span><span class="ls6 v7">1</span></div><div class="t m0 x7 h10 y5b ff8 fs1 fc0 sc0 ls1c">4<span class="ffb ls2e v6">\u2212</span><span class="ls6 v7">1</span></div><div class="t m0 x1b h10 y5b ff8 fs1 fc0 sc0 ls2f">8<span class="ls20 v6">+</span><span class="ls6 v7">1</span></div><div class="t m0 x1c h11 y5b ff8 fs1 fc0 sc0 ls6 ws40">16<span class="blank"> </span><span class="ls30 v6">+</span><span class="ffb ws38 v6">·<span class="blank"> </span>·<span class="blank"> </span>·</span></div><div class="t m0 x17 hd y5c ff8 fs1 fc0 sc0 ls6 ws41">c)<span class="blank"> </span>0<span class="ffa ls21">,</span><span class="ls22 ws3a">1+0<span class="blank _11"></span><span class="ffa ls6 ws31">,<span class="ff8 ws35">01<span class="blank"> </span>+<span class="blank"> </span>0</span><span class="ls21">,</span><span class="ff8 ws35">001<span class="blank"> </span>+<span class="blank"> </span>0</span><span class="ls21">,</span><span class="ff8 ws35">0001<span class="blank"> </span>+<span class="blank"> </span><span class="ffb ws38">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></span></span></div><div class="t m0 x17 hf y5d ff8 fs1 fc0 sc0 ls6 ws35">d)<span class="blank _13"> </span>1<span class="blank"> </span>+<span class="blank _16"> </span><span class="v6">1</span></div><div class="t m0 x1d h17 y5e ffb fs1 fc0 sc0 ls16">\u221a<span class="ff8 ls1c v9">2<span class="ls1d va">+<span class="ls6 v6">1</span></span></span></div><div class="t m0 x1e h10 y5f ff8 fs1 fc0 sc0 ls1c">2<span class="ls31 v6">+</span><span class="ls6 v7">1</span></div><div class="t m0 x18 h18 y60 ff8 fs1 fc0 sc0 ls6 ws2f">2<span class="ffb ws2b v3">\u221a</span><span class="ls1c">2<span class="ls2c va">+</span></span><span class="ffb ws38 va">·<span class="blank"> </span>·<span class="blank"> </span>·</span></div><div class="t m0 x1f h5 y20 ff5 fs3 fc0 sc0 ls6"><span class="fc1 sc0">3</span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w3 h9" data-page-no="4"><div class="pc pc4 w3 h9"><img fetchpriority="low" loading="lazy" class="bi x1 y61 w5 h19" alt="" src="https://files.passeidireto.com/0ea882e0-1852-4606-b90a-e77f5f4384fd/bg4.png"><div class="t m0 x2 hd y62 ff8 fs1 fc0 sc0 ls6 ws42">7.<span class="blank _1"> </span>La<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>in\ufb01nitos<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>una<span class="blank"> </span>progresi´<span class="blank _a"></span>on<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etrica<span class="blank"> </span>decrecien<span class="blank _0"></span>te<span class="blank"> </span>es<span class="blank"> </span>32.</div><div class="t m0 x3 hd y63 ff8 fs1 fc0 sc0 ls6 ws27">El<span class="blank"> </span>segundo<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>ermino<span class="blank"> </span>es<span class="blank"> </span>8.<span class="blank"> </span>Escrib<span class="blank _c"> </span>e<span class="blank"> </span>los<span class="blank"> </span>5<span class="blank"> </span>primeros<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>la<span class="blank"> </span>progresi´<span class="blank _a"></span>on.</div><div class="t m0 x2 hd y64 ff8 fs1 fc0 sc0 ls6 ws43">8.<span class="blank _1"> </span>Una<span class="blank"> </span>persona<span class="blank"> </span>infectada<span class="blank"> </span>p<span class="blank _c"> </span>or<span class="blank"> </span>un<span class="blank"> </span>virus<span class="blank"> </span>lo<span class="blank"> </span>contagia<span class="blank"> </span>a<span class="blank _8"> </span>cuatro<span class="blank"> </span>p<span class="blank _c"> </span>ersonas.<span class="blank"> </span>Al<span class="blank"> </span>cab<span class="blank _c"> </span>o<span class="blank"> </span>de<span class="blank"> </span>1</div><div class="t m0 x3 hd y65 ff8 fs1 fc0 sc0 ls6 ws44">hora<span class="blank"> </span>cada<span class="blank"> </span>una<span class="blank"> </span>se<span class="blank"> </span>lo<span class="blank"> </span>ha<span class="blank"> </span>con<span class="blank _0"></span>tagiado<span class="blank"> </span>a<span class="blank"> </span>otras<span class="blank"> </span>cuatro.<span class="blank"> </span>Sup<span class="blank _c"> </span>oniendo<span class="blank"> </span>que<span class="blank"> </span>cada<span class="blank"> </span>hora<span class="blank"> </span>se<span class="blank"> </span>ha</div><div class="t m0 x3 hd y66 ff8 fs1 fc0 sc0 ls6 ws45">rep<span class="blank _c"> </span>etido<span class="blank"> </span>la<span class="blank"> </span>operaci´<span class="blank _b"></span>on<span class="blank"> </span>inde\ufb01nidamen<span class="blank _0"></span>te,<span class="blank"> </span>¿cu´<span class="blank _a"></span>an<span class="blank _0"></span>to<span class="blank"> </span>tiemp<span class="blank _c"> </span>o<span class="blank"> </span>tardar´<span class="blank _a"></span>a<span class="blank"> </span>en<span class="blank"> </span>contagiarse<span class="blank"> </span>una</div><div class="t m0 x3 hd y67 ff8 fs1 fc0 sc0 ls6 ws28">ciudad<span class="blank"> </span>de<span class="blank"> </span>21845<span class="blank"> </span>p<span class="blank _c"> </span>ersonas?</div><div class="t m0 x20 h1a y68 ffe fs0 fc0 sc0 ls6">Soluciones</div><div class="t m0 x2 h12 y69 ff8 fs1 fc0 sc0 ls6 ws46">1.<span class="blank _1"> </span>a)<span class="blank"> </span>Es<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etrica.<span class="blank"> </span>Raz´<span class="blank _a"></span>on<span class="blank"> </span><span class="ffa ls28">r</span><span class="ls29">=</span><span class="v6">1</span></div><div class="t m0 x21 h10 y6a ff8 fs1 fc0 sc0 ls32">2<span class="ls6 ws46 v6">;<span class="blank"> </span>b)<span class="blank"> </span>Es<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etrica.<span class="blank"> </span>Raz´<span class="blank _a"></span>on<span class="blank"> </span><span class="ffa ls28">r<span class="ff8 ls33">=<span class="ffb ls34">\u2212</span><span class="ls6 v6">1</span></span></span></span></div><div class="t m0 x22 h13 y6a ff8 fs1 fc0 sc0 ls35">4<span class="ls6 ws47 v6">;<span class="blank"> </span>c)<span class="blank"> </span>No<span class="blank"> </span>es<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etri-</span></div><div class="t m0 x3 he y6b ff8 fs1 fc0 sc0 ls6 ws27">ca;<span class="blank"> </span>d)<span class="blank"> </span>Es<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etrica.<span class="blank"> </span>Raz´<span class="blank _a"></span>on<span class="blank"> </span><span class="ffa ls36">r</span><span class="ls37">=<span class="ffb ls16 v3">\u221a</span></span>2.</div><div class="t m0 x2 hd y6c ff8 fs1 fc0 sc0 ls6 ws48">2.<span class="blank"> </span><span class="ffb ls38">{</span><span class="ws27">6,<span class="blank"> </span>12,<span class="blank"> </span>24,<span class="blank"> </span>48<span class="ffb">}</span></span></div><div class="t m0 x2 hd y6d ff8 fs1 fc0 sc0 ls6 ws48">3.<span class="blank"> </span><span class="ffa ls28">r</span><span class="ws3e">=<span class="blank"> </span>3.<span class="blank _6"> </span><span class="ffa ls17">a<span class="ffd fs5 ls27 v4">8</span></span><span class="ws49">=<span class="blank _7"> </span>177<span class="blank"> </span>147.</span></span></div><div class="t m0 x2 h12 y6e ff8 fs1 fc0 sc0 ls6 ws4a">4.<span class="blank _1"> </span>a)<span class="blank"> </span><span class="ffa ls39">S<span class="ffd fs5 ls27 v4">6</span></span><span class="ws3e">=<span class="blank"> </span>252;<span class="blank _9"> </span>b)<span class="blank _6"> </span><span class="ffa ls39">S<span class="ffd fs5 ls27 v4">7</span></span><span class="ls29">=</span><span class="v6">1093</span></span></div><div class="t m0 x23 h10 y6f ff8 fs1 fc0 sc0 ls3a">9<span class="ls6 ws27 v6">;<span class="blank"> </span>c)<span class="blank"> </span><span class="ffa ws31">S<span class="ffd fs5 ls3b v4">4</span><span class="ff8 ls29">=<span class="ls6 v6">609</span></span></span></span></div><div class="t m0 x24 h13 y6f ff8 fs1 fc0 sc0 ls6 ws4b">200<span class="blank"> </span><span class="ws27 v6">;<span class="blank"> </span>d)<span class="blank"> </span><span class="ffa ls39">S<span class="ffd fs5 ls27 v4">5</span></span><span class="ws3e">=<span class="blank"> </span>1<span class="ffa ls23">,</span></span>1528;<span class="blank"> </span>e)<span class="blank"> </span><span class="ffa ws31">S<span class="ffd fs5 ws4c v4">10<span class="blank"> </span></span></span><span class="ws3e">=<span class="blank"> </span>0.</span></span></div><div class="t m0 x2 hf y70 ff8 fs1 fc0 sc0 ls6 ws48">5.<span class="blank"> </span><span class="ffa ls17">a<span class="ffd fs5 ls27 v4">6</span></span><span class="ls29">=</span><span class="v6">1</span></div><div class="t m0 x25 h1b y71 ff8 fs1 fc0 sc0 ls32">8<span class="ls3c v6">.<span class="ffa ls39">S<span class="ffd fs5 ls27 v4">6</span><span class="ff8 ls29">=<span class="ls6 v6">63</span></span></span></span></div><div class="t m0 x26 hd y71 ff8 fs1 fc0 sc0 ls6">8</div><div class="t m0 x2 hf y72 ff8 fs1 fc0 sc0 ls6 ws4a">6.<span class="blank _1"> </span>a)<span class="blank"> </span><span class="ffa ls3d">S</span><span class="ws3e">=<span class="blank"> </span>16;<span class="blank _9"> </span>b)<span class="blank _4"> </span><span class="ffa ls3d">S</span><span class="ls29">=</span><span class="v6">2</span></span></div><div class="t m0 x27 h10 y73 ff8 fs1 fc0 sc0 ls32">3<span class="ls6 ws27 v6">;<span class="blank"> </span>c)<span class="blank"> </span><span class="ffa ls3e">S<span class="ff8 ls29">=<span class="ls6 v6">1</span></span></span></span></div><div class="t m0 x13 h1c y73 ff8 fs1 fc0 sc0 ls35">9<span class="ls6 ws27 v6">;<span class="blank"> </span>d)<span class="blank"> </span><span class="ffa ls3e">S<span class="ff8 ls3f">=<span class="ffb ls16 vb">\u221a</span><span class="ls6 v6">2</span></span></span></span></div><div class="t m0 x28 h1d y74 ffb fs1 fc0 sc0 ls6 ws2b">\u221a<span class="ff8 ls40 v9">2</span><span class="ls41 v9">\u2212<span class="ff8 ls42">1<span class="ls6 ws35 va">=<span class="blank _7"> </span>2<span class="blank"> </span>+<span class="blank"> </span></span></span></span><span class="v3">\u221a</span><span class="ff8 vc">2</span></div><div class="t m0 x2 hd y75 ff8 fs1 fc0 sc0 ls6 ws48">7.<span class="blank"> </span><span class="ffb ls38">{</span><span class="ws27">16,<span class="blank"> </span>8,<span class="blank"> </span>4,<span class="blank"> </span>2,<span class="blank"> </span>1<span class="ffb">}</span></span></div><div class="t m0 x2 hd y76 ff8 fs1 fc0 sc0 ls6 ws48">8.<span class="blank"> </span><span class="ffa ls43">t</span><span class="ws3e">=<span class="blank"> </span>8<span class="blank _6"> </span>horas.</span></div><div class="t m0 x29 hf y77 ffa fs1 fc0 sc0 ls17">a<span class="ffc fs5 ls18 v4">n</span><span class="ff8 ls37">=</span>a<span class="ffd fs5 ls44 v4">1</span><span class="ffb ls45">·</span><span class="ls46">r<span class="ffc fs5 ls47 v8">n<span class="fff ls6 ws4d">\u2212<span class="ffd ls48">1</span></span></span><span class="ls39">S<span class="ffc fs5 ls18 v4">n</span><span class="ff8 ls29">=</span></span></span><span class="v6">a</span><span class="ffc fs5 ls49 vd">n</span><span class="ffb ls19 v6">·</span><span class="ls4a v6">r<span class="ffb ls41">\u2212</span></span><span class="v6">a</span><span class="ffd fs5 ls6 vd">1</span></div><div class="t m0 x2a h1e y78 ffa fs1 fc0 sc0 ls4b">r<span class="ffb ls41">\u2212<span class="ff8 ls4c">1</span></span><span class="ls3e v6">S<span class="ff8 ls4d">=</span></span><span class="ls6 ws31 v7">a<span class="ffd fs5 v4">1</span></span></div><div class="t m0 x2b hd y78 ff8 fs1 fc0 sc0 ls4e">1<span class="ffb ls41">\u2212<span class="ffa ls6">r</span></span></div><div class="t m0 x2c hd y79 ff8 fs1 fc0 sc0 ls6"><span class="fc1 sc0">2</span></div><div class="t m0 x1f h5 y20 ff5 fs3 fc0 sc0 ls6"><span class="fc1 sc0">4</span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf5" class="pf w3 h9" data-page-no="5"><div class="pc pc5 w3 h9"><img fetchpriority="low" loading="lazy" class="bi x20 y7a w6 h1f" alt="" src="https://files.passeidireto.com/0ea882e0-1852-4606-b90a-e77f5f4384fd/bg5.png"><div class="t m0 x2d hc y7b ff10 fs0 fc0 sc0 ls6 ws4e">Sucesiones<span class="blank"> </span>y<span class="blank"> </span>progresiones</div><div class="t m0 x2 hd y7c ff11 fs1 fc0 sc0 ls6 ws27">1.<span class="blank _1"> </span>Calcula<span class="blank"> </span>los<span class="blank"> </span>cinco<span class="blank"> </span>primeros<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>las<span class="blank"> </span>sucesiones:</div><div class="t m0 x5 h20 y7d ff12 fs1 fc0 sc0 ls17">a<span class="ff11 ls4f">)</span>a<span class="ffc fs5 ls18 v4">n</span><span class="ff11 ls6 ws3e">=<span class="blank"> </span>2</span><span class="ls50">n<span class="ff13 ls41">\u2212<span class="ff11 ls6 ws2f">9</span></span><span class="ls6 ws4f">,<span class="blank"> </span>b<span class="ff11 ls4f">)</span><span class="ls51">b<span class="ffc fs5 ls18 v4">n</span></span><span class="ff11 ws2e">=<span class="blank _7"> </span>1<span class="blank"> </span><span class="ff13 ls41">\u2212</span><span class="ws2f">5</span></span>n,<span class="blank"> </span>c<span class="ff11 ls4f">)</span><span class="ls52">c<span class="ffc fs5 ls18 v4">n</span><span class="ff11 ls33">=</span><span class="ls21">n</span></span><span class="ff14 fs5 v8">2</span></span></span></div><div class="t m0 x12 h20 y7d ff13 fs1 fc0 sc0 ls41">\u2212<span class="ff11 ls6 ws2f">2<span class="ff12 ws4f">,<span class="blank"> </span>d</span><span class="ls4f">)<span class="ff12 ls53">d<span class="ffc fs5 ls18 v4">n</span></span></span><span class="ws3e">=<span class="blank"> </span>2<span class="ff12 ls21">n</span><span class="ff14 fs5 v8">2</span></span></span></div><div class="t m0 x2e hd y7d ff13 fs1 fc0 sc0 ls41">\u2212<span class="ff12 ls50">n</span>\u2212<span class="ff11 ls6">3</span></div><div class="t m0 x2 hd y7e ff11 fs1 fc0 sc0 ls6 ws27">2.<span class="blank _1"> </span>Calcula<span class="blank"> </span>el<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>ermino<span class="blank"> </span><span class="ff12 ls17">a</span><span class="ff14 fs5 ws50 v4">20<span class="blank"> </span></span>de<span class="blank"> </span>las<span class="blank"> </span>progresiones<span class="blank"> </span>aritm<span class="blank _0"></span>´<span class="blank _b"></span>eticas<span class="blank"> </span>siguien<span class="blank _0"></span>tes:</div><div class="t m0 x2f hd y7f ff11 fs1 fc0 sc0 ls6 ws51">a)<span class="blank"> </span>2<span class="ff12 ls23">,</span><span class="ws2f">4<span class="ff12 ls23">,</span>6<span class="ff12 ls23">,</span>8<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x2f hd y80 ff11 fs1 fc0 sc0 ls6 ws52">b)<span class="blank"> </span><span class="ff13 ws31">\u2212</span><span class="ws2f">1<span class="ff12 ls23">,<span class="ff13 ls12">\u2212</span></span>2<span class="ff12 ls23">,</span><span class="ff13 ws31">\u2212</span>3<span class="ff12 ls24">,</span><span class="ff13 ws31">\u2212</span>4<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x2f hd y81 ff11 fs1 fc0 sc0 ls6 ws53">c)<span class="blank"> </span>3<span class="ff12 ls23">,</span><span class="ws2f">8<span class="ff12 ls23">,</span>13<span class="ff12 ls23">,</span>18<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x2f hd y82 ff11 fs1 fc0 sc0 ls6 ws54">d)<span class="blank"> </span>7<span class="ff12 ls23">,</span><span class="ws2f">5<span class="ff12 ls23">,</span>3<span class="ff12 ls23">,</span>1<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x2 hd y83 ff11 fs1 fc0 sc0 ls6 ws55">3.<span class="blank _1"> </span>De<span class="blank"> </span>las<span class="blank"> </span>progresiones<span class="blank"> </span>aritm<span class="blank _0"></span>´<span class="blank _b"></span>eticas<span class="blank"> </span>del<span class="blank"> </span>problema<span class="blank"> </span>an<span class="blank _0"></span>terior<span class="blank"> </span>calcula<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los</div><div class="t m0 x3 hd y84 ff11 fs1 fc0 sc0 ls6 ws27">v<span class="blank _0"></span>ein<span class="blank _0"></span>te<span class="blank"> </span>primeros<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos.</div><div class="t m0 x2 hd y85 ff11 fs1 fc0 sc0 ls6 ws27">4.<span class="blank _1"> </span>Calcula<span class="blank"> </span>el<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>ermino<span class="blank"> </span><span class="ff12 ls17">a</span><span class="ff14 fs5 ws50 v4">10<span class="blank"> </span></span>de<span class="blank"> </span>las<span class="blank"> </span>progresiones<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etricas<span class="blank"> </span>siguien<span class="blank _0"></span>tes</div><div class="t m0 x30 hd y86 ff11 fs1 fc0 sc0 ls6 ws56">a)<span class="blank"> </span>1<span class="ff12 ls23">,</span><span class="ws2f">2<span class="ff12 ls23">,</span>4<span class="ff12 ls23">,</span>8<span class="ff12 ls23">,</span>16<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x30 hd y87 ff11 fs1 fc0 sc0 ls6 ws57">b)<span class="blank"> </span>2<span class="ff12 ls23">,<span class="ff13 ls12">\u2212</span></span><span class="ws2f">2<span class="ff12 ls23">,</span>2<span class="ff12 ls23">,<span class="ff13 ls12">\u2212</span></span>2<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x30 hd y88 ff11 fs1 fc0 sc0 ls6 ws41">c)<span class="blank"> </span>3<span class="ff12 ls23">,</span><span class="ws2f">6<span class="ff12 ls23">,</span>12<span class="ff12 ls23">,</span>24<span class="ff12 ls23">,</span>48<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x30 hd y89 ff11 fs1 fc0 sc0 ls6 ws58">d)<span class="blank"> </span>2<span class="ff12 ls23">,</span><span class="ws2f">6<span class="ff12 ls23">,</span>18<span class="ff12 ls23">,</span>54<span class="ff12 ls23">,</span><span class="ff13 ws29">·<span class="blank"> </span>·<span class="blank"> </span>·</span></span></div><div class="t m0 x2 hd y8a ff11 fs1 fc0 sc0 ls6 ws59">5.<span class="blank _1"> </span>Calcula<span class="blank"> </span>la<span class="blank"> </span>suma<span class="blank"> </span>de<span class="blank"> </span>los<span class="blank"> </span>10<span class="blank"> </span>primeros<span class="blank"> </span>t<span class="blank _0"></span>´<span class="blank _b"></span>erminos<span class="blank"> </span>de<span class="blank"> </span>las<span class="blank"> </span>progresiones<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etricas</div><div class="t m0 x3 hd y8b ff11 fs1 fc0 sc0 ls6 ws2f">an<span class="blank _0"></span>teriores.</div><div class="t m0 x1 hf y8c ff11 fs1 fc0 sc0 ls6 ws27">Progresiones<span class="blank"> </span>aritm<span class="blank _0"></span>´<span class="blank _b"></span>eticas.<span class="blank _17"> </span><span class="ff12 ls17">a<span class="ffc fs5 ls18 v4">n</span></span><span class="ls33">=<span class="ff12 ls17">a<span class="ff14 fs5 ls44 v4">1</span></span></span><span class="ws35">+<span class="blank"> </span>(<span class="ff12 ls50">n<span class="ff13 ls41">\u2212</span></span><span class="ws5a">1)<span class="blank"> </span><span class="ff13 ls45">·</span><span class="ff12 ws31">d</span><span class="ls54">,</span><span class="ff12 ws31">S<span class="ffc fs5 ls18 v4">n</span></span><span class="ls29">=<span class="ls55 v6">(<span class="ff12 ls17">a<span class="ff14 fs5 ls44 v4">1</span><span class="ff11 ls56">+</span>a<span class="ffc fs5 ls57 v4">n</span><span class="ff11 ls58">)<span class="ff13 ls45">·</span></span><span class="ls6">n</span></span></span></span></span></span></div><div class="t m0 x31 hd y8d ff11 fs1 fc0 sc0 ls6">2</div><div class="t m0 x1 h21 y8e ff11 fs1 fc0 sc0 ls6 ws27">Progresiones<span class="blank"> </span>geom<span class="blank _0"></span>´<span class="blank _b"></span>etricas.<span class="blank _17"> </span><span class="ff12 ls17">a<span class="ffc fs5 ls18 v4">n</span></span><span class="ls33">=<span class="ff12 ls17">a<span class="ff14 fs5 ls44 v4">1</span><span class="ff13 ls19">·</span><span class="ls59">r</span></span></span><span class="ffc fs5 ws4d v5">n<span class="fff">\u2212<span class="ff14 ls5a">1</span></span></span><span class="ls5b">,<span class="ff12 ls39">S<span class="ffc fs5 ls18 v4">n</span></span><span class="ls29">=<span class="ff12 ls17 v6">a</span></span></span><span class="ffc fs5 vd">n</span></div><div class="t m0 x32 h22 y8f ff13 fs1 fc0 sc0 ls19">·<span class="ff12 ls4b">r</span><span class="ls5c">\u2212<span class="ff12 ls6 ws31">a<span class="ff14 fs5 v4">1</span></span></span></div><div class="t m0 x33 hd y90 ff12 fs1 fc0 sc0 ls4b">r<span class="ff13 ls41">\u2212<span class="ff11 ls6">1</span></span></div><div class="t m0 x1f h5 y20 ff4 fs3 fc0 sc0 ls6 wsd"><span class="fc1 sc0">3</span><span class="blank _5"></span><span class="ff5"><span class="fc1 sc0">5</span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf6" class="pf w3 h9" data-page-no="6"><div class="pc pc6 w3 h9"><img fetchpriority="low" loading="lazy" class="bi x34 y91 w7 h23" alt="" src="https://files.passeidireto.com/0ea882e0-1852-4606-b90a-e77f5f4384fd/bg6.png"><div class="t m0 x20 h24 y92 ffe fs6 fc0 sc0 ls6">Soluciones</div><div class="t m0 x1 hd y93 ff11 fs1 fc0 sc0 ls6 ws27">(1)<span class="blank"> </span>a)<span class="blank"> </span><span class="ff13 ws31">\u2212</span><span class="ws2f">7<span class="ff12 ls24">,</span><span class="ff13 ws31">\u2212</span>5<span class="ff12 ls23">,<span class="ff13 ls12">\u2212</span></span>3<span class="ff12 ls23">,</span><span class="ff13 ws31">\u2212</span>1<span class="ff12 ls24">,</span>1</span></div><div class="t m0 x1 hd y94 ff11 fs1 fc0 sc0 ls6 ws5b">b)<span class="blank"> </span><span class="ff13 ws31">\u2212</span><span class="ws2f">4<span class="ff12 ls23">,<span class="ff13 ls12">\u2212</span></span>9<span class="ff12 ls23">,</span><span class="ff13 ws31">\u2212</span>14<span class="ff12 ls24">,</span><span class="ff13 ws31">\u2212</span>19<span class="ff12 ls23">,<span class="ff13 ls12">\u2212</span></span>24</span></div><div class="t m0 x1 hd y95 ff11 fs1 fc0 sc0 ls6 ws5c">c)<span class="blank"> </span><span class="ff13 ws31">\u2212</span><span class="ws2f">1<span class="ff12 ls24">,</span>2<span class="ff12 ls23">,</span>7<span class="ff12 ls23">,</span>14<span class="ff12 ls23">,</span>23</span></div><div class="t m0 x1 hd y96 ff11 fs1 fc0 sc0 ls6 ws5b">d)<span class="blank"> </span><span class="ff13 ws31">\u2212</span><span class="ws2f">2<span class="ff12 ls23">,</span>3<span class="ff12 ls23">,</span>12<span class="ff12 ls24">,</span>25<span class="ff12 ls23">,</span>42</span></div><div class="t m0 x1 hd y97 ff11 fs1 fc0 sc0 ls6 ws27">(2)<span class="blank"> </span>a)<span class="blank"> </span>40,<span class="blank"> </span>b)<span class="blank"> </span><span class="ff13 ls12">\u2212</span>20,<span class="blank"> </span>c)<span class="blank"> </span>98,<span class="blank"> </span>d)<span class="blank"> </span><span class="ff13 ws31">\u2212</span>31</div><div class="t m0 x1 hd y98 ff11 fs1 fc0 sc0 ls6 ws27">(3)<span class="blank"> </span>a)<span class="blank"> </span>420,<span class="blank"> </span>b)<span class="blank"> </span><span class="ff13 ls12">\u2212</span>210,<span class="blank"> </span>c)<span class="blank"> </span>1010,<span class="blank"> </span>d)<span class="blank"> </span><span class="ff13 ws31">\u2212</span>240</div><div class="t m0 x1 hd y99 ff11 fs1 fc0 sc0 ls6 ws27">(4)<span class="blank"> </span>a)<span class="blank"> </span>512,<span class="blank"> </span>b)<span class="blank"> </span><span class="ff13 ls12">\u2212</span>2,<span class="blank"> </span>c)<span class="blank"> </span>1536,<span class="blank"> </span>d)<span class="blank"> </span>39366</div><div class="t m0 x1 hd y9a ff11 fs1 fc0 sc0 ls6 ws27">(5)<span class="blank"> </span>a)<span class="blank"> </span>1023,<span class="blank"> </span>b)<span class="blank"> </span>0,<span class="blank"> </span>c)<span class="blank"> </span>3069,<span class="blank"> </span>d)<span class="blank"> </span>59048</div><div class="t m0 x35 hd y9b ff11 fs1 fc0 sc0 ls6"><span class="fc1 sc0">2</span></div><div class="t m0 x1f h5 y20 ff4 fs3 fc0 sc0 ls6 wsd"><span class="fc1 sc0">4</span><span class="blank _5"></span><span class="ff5"><span class="fc1 sc0">6</span></span></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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