Question

dada a P.G (12,-24,48,...)determine seu 10° termo ​

Answer 1

Vamos começar calculando a razão (q):

$razao\,(q)~=~\frac{a_2}{a_1}\\\\\\razao\,(q)~=~\frac{-24}{12}\\\\\\\boxed{razao\,(q)~=~-2}$

Agora, utilizando a equação do termo geral, podemos determinar o 10° termo:

$a_n~=~a_1~.~q^{n-1}\\\\\\a_{10}~=~a_1~.~q^{10-1}\\\\\\a_{10}~=~12~.~(-2)^9\\\\\\a_{10}~=~12~.~(-512)\\\\\\\boxed{a_{10}~=~-6144}$