Question

Find the common ratio and ${10}^{th}$ 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$=t_n=a{r}^{n-1}$

$\therefore t_{10}=\frac{-2}{3}\times 9^{10-1}$

$t_{10}=-2\times 3^{-1}\times 3^{2\times 9}$

$t_{10}=-2\times 3^{-1+18}$

$\therefore t_{10}=-2\times 3^{17}$