Question

Find nth term of the $G.P.\sqrt{3},\frac{1}{\sqrt{3}},\frac{1}{3\sqrt{3}},.....$

Answer 1

Find $n^{th}$ term of G.P. $\sqrt{3},\frac{1}{\sqrt{3}},\frac{1}{3\sqrt{3}},$ _ _ _

$a=\sqrt{3}$

$r=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}$

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

$=\sqrt{3}(\frac{1}{3}{)}^{n-1}$

$=\sqrt{3}(\frac{1}{3}{)}^n.(\frac{1}{3}{)}^{-1}$

$=\sqrt{3}\left(\frac{1}{3}{)}^n\right(3)$

$t_n=3\sqrt{3}(1/3{)}^n$