Question

Find the common ratio and general term of the G.P $1,\frac{-1}{2},\frac{1}{4},\frac{-1}{8},,...$

Answer 1

Given series $1,\frac{-1}{2},\frac{1}{4},\frac{-1}{8},,...$ is in G.P

First term$a=1$

Common ratio$r=\frac{\frac{1}{4}}{\frac{-1}{2}}$

$r=\frac{1}{4}\times -2$

$r=\frac{-1}{2}$

General term$=a_n=a.r^{n-1}$

$a_n=1{\left(\frac{-1}{2}\right)}^{n-1}$

$a_n={(-1)}^{n-1}{\left(\frac{1}{2}\right)}^{n-1}$

$a_n={\left(\frac{-1}{2}\right)}^{n-1}$