Question

In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.

Answer 1

Let the first term is a and the common ratio is r

Then,

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

and $a{r}^5=192$ ........... (ii)

Dividing (ii) by (i), we get

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

$r^3=8$

$r=2$

Now,

$a{r}^2=24$

$\Rightarrow a{.2}^2=24$

$\Rightarrow a=6$

Thus the ${10}^{th}$ term will be $a{r}^9={6.2}^9=3072$