Question

In G.P $3rd$ term is $24$ and $6th$ term is 192 then find $10th$ term

Answer 1

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

$a_3=a{r}^2=24$...(1)

$a_6=a{r}^5=192$...(2)

dividing (2) by (1) we get

$\frac{a{r}^5}{a{r}^2}=\frac{192}{24}$

$r^3=8\Rightarrow r=2$

From (1)

$a{r}^2=24$

$a=\frac{24}{2^2}=6$

$\therefore a_{10}=\left(6\right)(2{)}^{10-1}=3072$