Question

quantos termos tem a pg (1/2 , 3/4 , ... ,81/32)

Answer 1

Olá^^

pelos dados da P.G.:

$\begin{cases}a_1= \dfrac{1}{2}\\\\ q= \dfrac{a_2}{a_1} = \dfrac{3}{4}\div \dfrac{1}{2}= \dfrac{3}{4}\cdot \dfrac{2}{1}= \dfrac{3}{2}\\\\a_n= \dfrac{81}{32}\\\\n=? \end{cases}$

Usando a fórmula do termo geral da P.G., teremos:

$a_n=a_1 \cdot q^{n-1}\\\\ \dfrac{81}{32}= \dfrac{1}{2}\cdot \dfrac{3}{2}^{n-1}\\\\ \dfrac{3}{2}^{n-1}= \dfrac{81}{32}\div \dfrac{1}{2}\\\\ \dfrac{3}{2}^{n-1}= \dfrac{162}{32}\\\\ \dfrac{3}{2}^{n-1}= \dfrac{81}{16}\\\\ \dfrac{3}{2}^{n-1}=\left( \dfrac{3}{2}\right)^4\\\\ n-1=4\\ n=4+1\\\\ \Large\boxed{\boxed{n=5~termos}}.\\.$

Tenha ótimos estudos ;D