Question

quantos termos possiu a PG o onde a1=6, an=384 e q=2​

Answer 1

Resposta:

Explicação passo-a-passo:

an = a1 . q^n-1

384 = 6 . 2^n-1

384/6 = 2^n-1

64 = 2^n-1

Fatorando o 64

64 = 2^6

2^6 = 2^n-1

Bases iguais, iguala os expoentes

6 = n - 1

n = 6 + 1

n = 7

Answer 2

Para determinarmos o numero "n" de termos dessa PG, podemos utilizar a equação do termo geral, acompanhe:

$a_n~=~a_1~.~q^{n-1}\\\\\\384~=~6~.~2^{n-1}\\\\\\2^{n-1}~=~\frac{384}{6}\\\\\\2^{n-1}~=~64\\\\\\2^{n-1}~=~2\,.\,2\,.\,2\,.\,2\,.\,2\,.\,2\\\\\\2^{n-1}~=~2^6\\\\\\2\!\!\!\backslash^{\,n-1}~=~2\!\!\!\backslash^{\,6}\\\\\\n-1~=~6\\\\\\\boxed{n~=~7~termos}$