Question

Find the common ratio and general term of a G.P $\frac{-2}{3},-6,-54,...$

Answer 1

Given series $\frac{-2}{3},-6,-54,...$ is in G.P

First term$=a=\frac{-2}{3}$

Common ratio$=\frac{-6}{\frac{-2}{3}}=\frac{-6\times 3}{-2}=9$

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

General term$=\frac{-2}{3}{9}^{n-1}$

General term$=-23^{-1}\times 3^{2n-2}$

General term$=-2\times 3^{-1+2n-2}$

General term$=-2\times 3^{2n-3}$