Question

In a G.P. if the $(m+n{)}^{th}$ term is p and $(m-n{)}^{th}$ term is q, then its $m^{th}$ term is

• A. 0
• B. pq
• C. $\sqrt{pq}$
• D. $\frac{1}{2}(p+q)$

Answer 1

The correct option is C

$\sqrt{pq}$

(c) $\sqrt{pq}$

Here, $a_{(}m+n)=p$

$\Rightarrow a{r}^{(}m+n-1)=p$ .....(i)

Also, $a_{(m-n)}=q$

$\Rightarrow a{r}^{(m-n-1)}=q$

Multiplying (i) and (ii) :

$\Rightarrow a{r}^{(m+n-1)}a{r}^{(m-n-1)}=pq$ $\Rightarrow a^2{r}^{(2m-2)}=pq$

$\Rightarrow (a{r}^{(m-1)}{)}^2=pq$ $\Rightarrow a{r}^{(m-1)}=\sqrt{pq}$

$\Rightarrow a_m=\sqrt{pq}$

Thus, the $m^{th}$ term is $\sqrt{pq}$.