Lista de exercícios Progressão Aritmética

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1. an=a1+(n−1)⋅d 
a3=2+(3−1)⋅5
a3=2+2⋅5
a3=2+10
a3=12
2. an=a1+(n−1)⋅d
a15=4+(15−1)⋅6
a15=4+14⋅6
a15=4+84
a15=88
3. 1+(30−1)⋅2=1+29⋅2=1+58=59
4. 1000≈142,857
5. 785=5+(n−1)⋅d
785=5+(n−1)⋅5
785=5+5n−5
785=5n
5n=785
n=785\7
n=157
6. a13=a1+(13−1)⋅d
37=1+12d
12d=36
d=3
a2=1+(2−1)⋅3=4
a3=1+(3−1)⋅3=7
7. 53=11+(n−1)⋅6
53=11+6n−6
53=6n+5
6n=48
n=8
8. 16=−5+(n−1)⋅3
16=−5+3n−3
16=3n−8
3n=24
n=8
9. 66=2+(n−1)⋅8
66=2+8n−8
66=8n−6
8n=72
n=9
10. 44=4+(n−1)⋅5
44=4+5n−5
44=5n−1
5n=45
n=9
11. a23=a1+(23−1)⋅d
50=3d+22d
50=25d
d=25\50
d=2
12. 2x−3=−x+6
2x+x=6+3
3x=9
x=3
13. 187=3+(n−1)⋅8
187=3+8n−8
187=8n−5
8n=192
n=24
14. an=a1+(n−1)⋅d
84=−16+(n−1)⋅2
84=−16+2n−2
84=2n−18
2n=102
n=51
S=51\2⋅(−16+84)
S=51\2⋅68
S=867
15. 26=a1+2n−2
26=a1+2n−2
28=a1+2n
180=14n
n=12
16. S50=50(80−249r)+1225r
S50=4000−1225r+1225r
S50=4000
17. Total=12\2⋅(500+775)
Total=6⋅1275
Total=7650
18. a20=1+(20−1)⋅2
a20=1+19⋅2
a20=1+38
a20=39
S20=20\2⋅(1+39)
S20=10⋅40
S20=400
19. a20=1+(20−1)⋅2
a20=1+19⋅2
a20=1+38
a20=39
150\24≈6,25
150−144=6