Question

Determine o 9° termo da PG em que:
$a5 = ab^{2} \: e \: q = \frac{1}{b}$

Answer 1

Podemos utilizar a equação do termo geral da PG:

$a_n=a_m.q^{n-m}\\\\a_9=a_5.q^{9-5}\\\\a_9=ab^2.\left(\frac{1}{b}\right)^4\\\\a_9=ab^2.\frac{1^4}{b^4}\\\\a_9=\frac{ab^2}{b^4}\\\\a_9=ab^{2-4}\\\\a_9=ab^{-2}\\\\a_9=\frac{a}{b^2}$