Question

calcule o oitavo termo da p.g (15,5,...)

Answer 1

Vamos começar determinando a razão (q) da PG:

$razao~=~\dfrac{a_2}{a_1}\\\\\\razao~=~\dfrac{5}{15}\\\\\\\boxed{razao~=~\dfrac{1}{3}}$

Agora, utilizando a equação do termo geral, podemos determinar o 8° termo da sequencia:

$a_n~=~a_1~.~q^{n-1}\\\\\\a_8~=~15~.~\left(\dfrac{1}{3}\right)^{8-1}\\\\\\a_8~=~15~.~\left(\dfrac{1}{3}\right)^{7}\\\\\\a_8~=~15~.~\dfrac{1^7}{3^7}\\\\\\a_8~=~15~.~\dfrac{1}{2187}\\\\\\\boxed{a_8~=~\dfrac{5}{729}}$

Answer 2

resolução!

q = a2 / a1

q = 5 / 15

q = 1/3

a8 = a1 * q^7

a8 = 15 * (1/3)^7

a8 = 15 * 1/2187

a8 = 15/2187

a8 = 5/729