Question

Numa PG decrescente 3 = −8 e 11 = −2048. Determine a razão, o termo 1 e escreva esta PG.​

Answer 1

Creio que você quis dizer a3 = -8 e a11 = -2048, certo!?

Utilizando a equação do termo geral, temos:

$a_n~=~a_m.q^{n-m}\\\\\\a_{11}~=~a_3.q^{11-3}\\\\\\-2048~=~-8.q^{8}\\\\\\q^{8}~=~\frac{-2048}{-8}\\\\\\q^{8}~=~256\\\\\\r~=~\sqrt[8]{256}\\\\\\r~=~\sqrt[8]{2^8}\\\\\\\boxed{r~=~2}$

Agora utilizando a equação do termo geral para achar a1:

$a_1~=~a_3.q^{1-3}\\\\\\a_1~=~-8~.~2^{-2}\\\\\\a_1~=~-8~.~\frac{1}{2^2}\\\\\\a_1~=~-8~.~\frac{1}{4}\\\\\\\boxed{a_1~=~-2}$

A PG fica: {-2 , -4 , -8 , -16 , -32 , -64 , -128 , -256 , -512 , -1024 , -2048}