Question

Quantos termos da P.G. (3,6,12,...) devemos somar a fim de obter soma igual a 14762?

Answer 1

Formula da soma de uma P.G: Soma = a₁*[ R^(n) - 1]/(r -1)

S = 14762
a₁ = 3
n = ?
R = a1/a2

/$\\ S = a1* (\frac{R^n - 1}{R - 1} ) \\ 14762 = 3* \frac{2^n - 1}{2 -1} \\ 14762 = \frac{3*2^n + 3*(-1)}{1} \\ 14762 = 3*2^n - 3 \\ 14762 = 3(2^n - 1) \\ \frac{14762}{3} = 2^n - 1 \\ \\ 2^n = \frac{14762}{3} + 1 \\ \\ 2^n = \frac{14762 + 3}{3} \\ \\ 2^n = \frac{14765}{3} \\ \\ log(2)^n = log( \frac{14765}{3}) \\ \\ n*log(2) = log( \frac{14765}{3} ) \\ \\ n = \frac{log( \frac{14765}{3}) }{log(2)} \\ \\ n = \frac{3,69211211966}{0,3010299957} = 12,2649$