Question

Qual é o 10°termo da P.G (20,10,5,...)

Answer 1

Termo geral da P.G:
$a_{n}=a_{1}.q^(^n^-^1^)$

P.G (20,10,5,...)

$a_{1}=20$;
$a_{2}=10$;
$a_{3}=5$.

$q=\frac{a_{2}}{a_{1}}$ =>
$q=\frac{10}{20}$ =>
$q=\frac{1}{2}$.

$a_{10}=20.\frac{1}{2}^(^10^-^1^)$ =>
$a_{10}=20.\frac{1}{2}^9$ =>
$a_{10}=20.\frac{1}{512}$ =>
$a_{10}=\frac{20}{512}$ =>
$a_{10}=\frac{5}{128}$.

O décimo termo dessa P.G é $\frac{5}{128}$!