Question

$3$ geometric means between $\frac{1}{9}$ and $9$ is

• A. $\frac{2}{3},1,3$
• B. $\frac{1}{3},2,3$
• C. $\frac{1}{3},1,6$
• D. $\frac{1}{3},1,3$

Answer 1

The correct option is D $\frac{1}{3},1,3$

Given, $\frac{1}{9},..,..,..,9$
$a=\frac{1}{9}$, $n=2+3=5$, $t_n=9$
We know, $t_n=a{r}^{n-1}$
$\therefore \frac{1}{9}\times r_{5-1}=9$
$\therefore r^4=81$
$\therefore r=3$
$1^{st}$ G.M $=\frac{1}{9}\times 3=\frac{1}{3}$

$2^{nd}$ G.M $=\frac{1}{3}\times 3=1$

$3^{rd}$ G.M $=3$