Question

Quantos termos tem a PG(1/2, 3/4,...,81/32)?

Por favor, com a resolução.

Answer 1

an=a1q^n-1
91/32=1/2(3/2)ñ-1
(n-1) log3/2=log81/16
n-1=log81/16:log3/2
n=5

Answer 2

E aí Erick, blz,

vamos identificar os termos desta P.G.,

$\begin{cases}a _{1}=1/2\\ q=a _{2}/a _{2}~\to~q=(3/4)/(1/2)~\to~q=3/2\\ A _{n}=81/32\\ n=?\end{cases}$

agora, usamos a fórmula do termo geral:

$\boxed{A _{n}=a _{1}*q ^{n-1}}\\\\ 81/32=(1/2)*(3/2) ^{n-1}\\\\ \frac{(81/32)}{(1/2)}=(3/2) ^{n-1}\\\\ \frac{162}{32}=(3/2) ^{n-1}\\\\ 81/16=(3/2) ^{n-1}\\ (3/2) ^{4}=(3/2) ^{n-1}\\ n-1=4\\\\ \boxed{n=5~termos}$


Espero ter ajudado você cara, e tenha ótimos estudos =))