Question

Calcule a soma dos termos da PG 4,8,...1024

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: geometrica \\ \\ q = \frac{a2}{a1} = \frac{8}{4} = 2 \\ \\ = = = = = = = = = = \\ \\ > \: numero \: de \: termos \: da \: pg \\ \\ an = a1 \times q {}^{n - 1} \\ 1024 = 4 \times 2 {}^{n - 1} \\ \frac{1024}{4} = 2 {}^{n - 1} \\ 256 = 2 {}^{n - 1} \\ 2 {}^{8} = 2 {}^{n - 1} \\ n - 1 = 8 \\ n = 8 + 1 \\ n = 9 \\ \\ = = = = = = = = = = \\ \\ > \: soma \: dos \: termos \: da \: pg \\ \\ sn = \frac{a1(q {}^{n} - 1)}{q - 1} \\ \\ sn = \frac{4(2 {}^{9} - 1)}{2 - 1} \\ \\ sn = \frac{4(512 - 1)}{1} \\ \\ sn = 4 \times 511 \\ \\ sn = 2044 \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant$