Question

Numa P.G de razao 4 o a1=8 é o ano=512 quantos termos tem essa P.G

Answer 1

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

P.G = { 8, 32,........., 512 }.


$a_{1}=8$;
$r=4$;
$a_{n}=512$;
$n=?$.

$512=8.4^(^n^-^1^)$ =>
$512=2^9$;
$8=2^3$;
$4=2^2$;
$4^-^1=\frac{1}{4}$.
$2^9=2^3.\frac{(2^2)^n}{2^2}$ =>
$\frac{2^9.2^2}{2^3}=(2^2)^n$ =>
$\frac{2^1^1}{2^3}=(2^2)^n$ =>
$2^8=(2^2)^n$ =>
$8=2.n$ =>
$n=\frac{8}{2}$ =>
$n=4$.

Essa P.G tem 4 termos!