Question

8- A soma dos n primeiros termos da IP.G(3,6,12,...) é *S_{n} = 765. Qual o valor de n?

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: geometrica \\ \\ q = \frac{a2}{a1} = \frac{6}{3} = 2 \\ \\ \\ sn = \frac{a1(q {}^{n} - 1)}{q - 1} \\ \\ 765 = \frac{3(2 {}^{n} - 1)}{2 - 1} \\ \\ 765 = \frac{3(2 {}^{n} - 1) }{1} \\ \\ \frac{765}{3} = 2 {}^{n} - 1 \\ \\ 255 = 2 {}^{n} - 1 \\ \\ 255 + 1 = 2 {}^{n} \\ \\ 256 = 2 {}^{n} \\ \\ 2 {}^{8} = 2 {}^{n} \\ \\ n = 8 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$