Question

determine o 8° termo da PG (1/16, 1/8, 1/4,...)

Answer 1

Progressão Geométrica:

Primeiro devemos encontrar a razão:

$\mathtt{q = A_2 \div A_1} \\ \\  \mathtt{q = \dfrac{1}{8} \div \dfrac{1}{16}~ \longrightarrow~ \dfrac{1}{8} \times \dfrac{16}{1} ~\longrightarrow ~ \dfrac{16}{8}~\longrightarrow ~2}$

Agora vamos aplicar o termo geral:

$\mathtt{A_n = A_1~.~q^{n-1}} \\ \\  \mathtt{A_{8}=\frac{1}{16}~.~2^{8-1}} \\ \\ \mathtt{A_8 = \frac{1}{16}~.~2^7} \\ \\ \mathtt{A_8 = \frac{1}{16}~.~128} \\ \\ \mathtt{A_8 = \frac{128}{16}} \\ \\ \mathtt{A_8 = 8} \\ \\ \\ \boxed{\boxed{\mathtt{Resposta: A_8 = 8}}}$