Question

determine a soma dos 8primdoros termos de cada pg (50,500,5000​

Answer 1

Vamos começar determinando a razão (q) da PG:

$razao\,(q)~=~\frac{a_2}{a_1}\\\\\\razao\,(q)~=~\frac{500}{50}\\\\\\\boxed{razao\,(q)~=~10}$

Agora, utilizando a equação da soma dos finitos termos da PG, temos:

$S_n~=~\frac{a_1.(q^n-1)}{q-1}\\\\\\S_8~=~\frac{50\,.\,(10^8-1)}{10-1}\\\\\\S_8~=~\frac{50\,.\,(100.000.000-1)}{9}\\\\\\S_8~=~\frac{50\,.\,(99.999.999)}{9}\\\\\\S_8~=~\frac{50\,.\,(11.111.11)}{1}\\\\\\\boxed{S_8~=~555.555.550}$