Question

Determine o 8 termo da PG (20,30,...)​

Answer 1

Vamos começar determinando a razão (q) da PG:

$q~=~\dfrac{a_2}{a_1}\\\\\\q~=~\dfrac{30}{20}\\\\\\\boxed{q~=~\dfrac{3}{2}}$

Utilizando a relação do termo geral da PG, temos:

$a_n~=~a_1\cdot q^{n-1}\\\\\\a_8~=~20\cdot \left(\dfrac{3}{2}\right)^{8-1}\\\\\\a_8~=~20\cdot \left(\dfrac{3}{2}\right)^{7}\\\\\\a_8~=~20\cdot \dfrac{3^7}{2^7}\\\\\\a_8~=~20\cdot \dfrac{2187}{128}\\\\\\a_8~=~\dfrac{43740}{128}\\\\\\a_8~=~\dfrac{43740~~\div4}{~~~128~~\div4}\\\\\\\boxed{a_8~=~\dfrac{10935}{32}}$