Question

o décimo termo da PG -1/7, -1/3​

Answer 1

Vamos começar determinando a razão da PG:

$razao~=~\dfrac{a_2}{a_1}\\\\\\razao~=~\dfrac{-\frac{1}{3}}{-\frac{1}{7}}\\\\\\razao~=~-\dfrac{1}{3}~.~\left(-\dfrac{7}{1}\right)\\\\\\\boxed{razao~=~\dfrac{7}{3}}$

Agora, utilizando a equação do termo geral da PG, podemos determinar o 10° termo:

$a_n~=~a_1~.~q^{n-1}\\\\\\a_{10}~=~a_1~.~q^{10-1}\\\\\\a_{10}~=~-\dfrac{1}{7}~.~\left(\dfrac{3}{7}\right)^{9}\\\\\\a_{10}~=~-\dfrac{1}{7}~.~\dfrac{3^9}{7^9}\\\\\\a_{10}~=~-\dfrac{3^9}{7^{9+1}}\\\\\\\boxed{a_{10}~=~-\dfrac{3^9}{7^{10}}}$