Question

Calcule o 122o. termo da PG (1, -1, 1, -1, 1, -1,...)

Answer 1

Vamos começar determinando a razão (q):

$q~=~\dfrac{a_{n+1}}{a_n}~=~\dfrac{a_2}{a_1}~=~\dfrac{-1}{1}~=~\boxed{-1}$

Utilizando a relação do termo geral da PG, temos:

$a_n~=~a_1\cdot q^{n-1}\\\\\\a_{122}~=~1\cdot (-1)^{122-1}\\\\\\a_{122}~=~(-1)^{121}\\\\\\\boxed{a_{122}~=\,-1}$