Question

Qual a soma dos sete primeiro termos da P.G (2, -6, 18,...)?
a) 1094
b) -1094
c) 1093
d) -1093
e) 2186​

Answer 1

$\boxed{\begin{array}{l}\underline{\rm Soma~dos~termos~da~PG~finita}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{a_1\cdot(q^n-1)}{q-1}}}}}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf (2,-6,18,...)\\\tt dados\begin{cases}\sf a_1=2\\\sf q=\dfrac{-6}{2}=-3\\\sf n=7\\\sf S_7=?\end{cases}\\\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf S_7=\dfrac{2\cdot((-3)^7-1)}{-3-1}\\\sf S_7=\dfrac{2\cdot(-2187-1)}{-4}\\\sf S_7=\dfrac{2\cdot-2188}{-4}\\\sf S_7=2\cdot547\\\sf S_7=1094\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$