Question

Extra Quantos termos tem uma P.G em que 01 = 3 an= 50421 e q=7​

Answer 1

Resposta:

Explicação passo a passo:

a₁ = 3

aₙ = 50421

q = 7​

Termo geral da PG

$7^{n-1}=\frac{7^n}{7^1} = \frac{7^n}{7}$

$a_n=a_1.q^{n-1}\\\\50421=3*7^{n-1}\\\\\frac{50421}{3} =7^{n-1}\\\\16807 = 7^{n-1}\\\\16807 = \frac{7^n}{7} \\\\16807 *7= 7^{n}\\\\117649=7^n\:\:\:\:logaritmo\:\:dos\:\:dois\:\:lados\\\\log117649=log7^n\\\\\\log117649=n.log7\\\\5,07=n*0,85\\\\\frac{5,07}{0,85} = n\\\\n = 6$

OBSERVAÇÃO

$7^{n-1}=\frac{7^n}{7^1} = \frac{7^n}{7}$