Question

Quantos termo tem a pg (2,4,8,...,1024)?

Answer 1

Oi!

PG(2, 4, 8, ..., 1024)

a1 = 2
q = 4/2 = 8/4 = 2
an = 1024
n = ?

Termo geral:
$\boxed{ a_n = a_1 \times {q}^{n - 1}}$

$a_n = 2 \times {2}^{(n - 1)} \\ 1024 = 2 \times {2}^{(n - 1)} \\ \frac{1024}{2} = {2}^{(n - 1)} \\ 512 = {2}^{(n - 1)} \\ 2^9 = {2}^{n - 1}$
Propriedade:
$\boxed{a^x = a^y <=> x = y}$
$9 = n - 1 \\ n = 9 + 1 \\ \boxed{n = 10}$

Resposta: 10 termos.

Bons estudos.