Question

Sabe-se que numa PG de 7 termos a razão é 3, o primeiro termo é 1/9. Qual é a soma desses termos dessa PG?

Answer 1

$n=7\\q=3\\a_1= \dfrac{1}{9} \\\\ S_n=?\\\\\\S_n= \dfrac{a_1\times(q^n-1)}{q-1} \\\\\\S_n= \dfrac{\dfrac{1}{9}\times(3^7-1)}{3-1} \to\\\\\\ S_n= \dfrac{\dfrac{1}{9}\times(2187-1)}{2} \to\\\\\\ S_n= \dfrac{\dfrac{1}{9}\times2186}{2} \to \\\\\\ S_n= \dfrac{\dfrac{2186}{9}}{2} \to \\\\\\ S_n=\dfrac{2186}{9}\times\dfrac{1}{2}\to \\\\\\S_n=\dfrac{2186}{18}\to\\\\\\ \boxed{S_n=\dfrac{1093}{9}}$