Para resolver essa questão, é importante entender que estamos lidando com duas progressões aritméticas de mesma razão. Isso significa que a diferença entre os termos consecutivos em ambas as progressões é a mesma. Dadas as progressões a, b, c e ab, bc, ca, podemos escrever: b - a = c - b bc - ab = ca - bc Agora, vamos simplificar essas equações: b - a = c - b 2b = a + c bc - ab = ca - bc b(c - a) = c(a - b) Substituindo 2b = a + c na segunda equação, temos: b(2b - 2c) = c(a - b) 2b² - 2bc = ca - cb 2b² - 2bc = ca - bc 2b² = c(a - b) 2b² = ca - cb 2b² = c(a - b) 2b² = -c(b - a) 2b² = -bc + ac 2b² = ac - bc 2b² = (a - b)c Agora, podemos substituir a equação 2b = a + c na expressão 2b² = (a - b)c: 2(a + c)² = (a - a - c)c 2(a² + 2ac + c²) = -c 2a² + 4ac + 2c² = -c 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a² + 4ac + 2c² + c = 0 2a