Question

Determine a soma dos oito primeiros termos de cada P.G 
A)  (3,12,48,...)    B)  (-4,8,-16,...)

Answer 1

Considerando :

$Sn=\frac{a1(q^n-1)}{q-1}$

Resolução:
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$a)\\\\a1=3\\a2=12\\q=\frac{12}{3}=4\\\\\boxed{S8=\frac{3.(4^8-1)}{4-1}=\frac{3.(65536-1)}{3}=\frac{196605}{3}=\boxed{65535}}$

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$b)\\a1=-4\\a2=8\\r=\frac{a2}{a1}=\frac{8}{-4}=-2\\\\\boxed{S8=\frac{-4([-2]^8-1)}{-2-1}=\frac{-4(256-1)}{-3}=\frac{-1020}{-3}=\boxed{340}}$