Question

In a $G.P$., if third term is $63$ and the sixth term is $1701$, find its $n^{th}$ term.

• A. $7(3{)}^n$
• B. $2(3{)}^n$
• C. $5(3{)}^n$
• D. $Noneofthese$

Answer 1

The correct option is A $7(3{)}^n$

Let first term be $a$,

And common ratio be $r$

According to question,

$a{r}^5=1701$ And, $a{r}^2=63$

On dividing both the terms we get,

$\frac{a{r}^5}{a{r}^2}=\frac{1701}{63}$

$⟹r^3=27$

$⟹r=3$

As, $a{r}^2=63$

$⟹a{.3}^2=63$

$⟹a=7$

Hence, $nth$ term $=a{r}^n=7(3{)}^n$