Question

Determine o 10º termo da PG (3,6,12,...). Marque a resposta correta.

Answer 1

$\text{Teorema para o c\'alculo do n-\'esimo termo de uma P.G:}\\\\\\\fbox{ a_n=a_{1}\cdot q^{n-1} }\\\\\\\text{Onde q representa a raz\~ao e}~a_1~\text{o primeiro termo.}\\\\\\\text{Descobrindo a raz\~ao:}\\\\\\a_1\cdot q=a_2\\\\3\cdot q=6\\\\q= \dfrac{6}{3}\\\\q=2$


$\text{Substituindo os dados no teorema teremos o seguinte:}\\\\\\a_{10}=3\cdot 2^{10-1}\\\\a_{10}=3\cdot 2^9\\\\a_{10}=3\cdot 512\\\\a_{10}=1536$