Question

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

• A. $\sqrt{\left(pq\right)}$
• B. $\sqrt{\left(p/q\right)}$
• C. $\sqrt{\left(q/p\right)}$
• D. p/q

Answer 1

The correct option is A $\sqrt{\left(pq\right)}$

Let first term and common ratio of the G.P are $a$ and $r$ respectively
$T_{m+n}=a{r}^{m+n-1}=pand{T}_{m-n}=a{r}^{m-n-1}=q$
Multiplying $a^2{r}^{2m-2}=pq$
$\therefore T_m=a{r}^{m-1}=\sqrt{\left(pq\right)}$