Question

A soma dos n primeiros termos da PG (4, -8, 16, ....) é Sn = 684, qual o valor de n?​

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: geometrica \\ \\ q = \frac{a2}{a1} = \frac{ - 8}{4} = - 2 \\ \\ = = = = = = = = = = = = = = = \\ \\ \\ sn = \frac{a1(q {}^{n} - 1)}{q - 1} \\ \\ 684 = \frac{4( - 2 {}^{n} - 1) }{ - 2 - 1} \\ \\ 684 = \frac{4( - 2 {}^{n} - 1) }{ - 3} \\ \\ - 2052 = 4( - 2 {}^{n} - 1) \\ \\ \frac{ - 2052}{4} = - 2 {}^{n} - 1 \\ \\ - 513 = - 2 {}^{n} - 1 \\ \\ - 513 + 1 = - 2 {}^{n} \\ \\ - 512 = - 2 {}^{n} \\ \\ - 2 {}^{9} = - 2 {}^{n} \\ \\ n = 9 \\ \\ \\ resposta \: > \: pg \: de \: 9 \: termos \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant$