Question

If the $4^{th}$ and $9^{th}$ terms of $GP$ are $108$ and $26244$,find the general term of the $GP$

Answer 1

According to the given data

Let a=first term,r=common ratio

$a{r}^3=108a{r}^8=26244$

Dividing these equations we get

$\frac{a{r}^8}{a{r}^3}=243\Rightarrow r^5=243\Rightarrow r^5=3^5\Rightarrow r=3$

$a\ast 3^3=108\Rightarrow a=4$

Hence, general Term of GP is $T_n=4\ast (3{)}^{n-1}$