Question

Numa PG (256,128,...),calcule a razão e o 8 termo

Answer 1

Olá,

dos dados..

$\begin{cases}a_1=256\\ q= \dfrac{a_2}{a_1} = \dfrac{128}{256}= \dfrac{128\div128}{256\div128}= \dfrac{1}{2}\\\\n=8~termos\\ a_8=? \end{cases}$

Usando a fórmula do termo geral..

$a_n=a_1\cdot q^{n-1}\\\\ a_8=256\cdot\left( \dfrac{1}{2}\right)^{8-1}\\\\ a_8=256\cdot\left( \dfrac{1}{2}\right)^7\\\\ a_8=256\cdot \dfrac{1}{128}\\\\ a_8= \dfrac{256}{128}\\\\ \Large\boxed{a_8=2 }$