Question

Determine a soma dos dez primeiros termos da PG (2,-4,8,-16,...). Marque a resposta correta.

Answer 1

$\text{Teorema para soma dos n termos de uma P.G finita:}\\\\{\boxed{S_n=\dfrac{a_1\cdot q^n-a_1}{q-1}}$


$\text{Onde}~a_1~\text{representa o primeiro termo, e q representa a raz\~ao.}\\\\\\\text{Descobrindo a raz\~ao (q):}\\\\a_1\cdot q=a_2\\\\\\2\cdot q=-4\\\\\\q=\dfrac{-4}{2}\\\\\\q=-2\\\\\\\text{Substituindo os valores no teorema:}\\\\\\ S_{10}= \dfrac{2\cdot(-2)^{10}-2}{-2-1}\\\\\\S_{10}=\dfrac{(2\cdot1024)-2}{-3}\\\\\\S_{10}=\dfrac{2048-2}{-3}\\\\\\S_{10}=\dfrac{2046}{-3}\\\\\\S_{10}=-682$