Question

calcule a soma dos oito primeiros termos da P.G (-5,-10,-20,...)

Answer 1

Soma

$\boxed{S_n=\frac{a_1(q^n-1)}{q-1}}$

Razão

$q=\frac{a_2}{a_1}\\\\ q=\frac{-10}{-5}\\\\ \boxed{q=2}$

Agora

$S_8 = \frac{-5(2^8-1)}{2-1}\\\\ S_8=\frac{-5(256-1)}{1}\\\\ S_8=-5(255)\\\\ \boxed{S_8=-1275}$