Question

The fifth term of a G.P. is $81$ and the second term is $24$; find the series.

Answer 1

$a,ar,a{r}^2,a{r}^3,...........,a{r}^{n-1}$ be the G.P. with common ratio $r$
And let $a_n$ be the $n^{th}$ term of G.P.
Given :
$a_5=a{r}^4=81$ ..........(i)
$a_2=ar=24$ .........(ii)
Divide the eqn (i) by (ii), we get
$r^3=\frac{27}{8}$
$r=\frac{3}{2}$
Putting the value of $r$ in the eqn. (ii), we get
$a\times \frac{3}{2}=24$
$a=16$
Thus, the series is $16,24,36,54,.........$