Question

If the $(p+q{)}^{th}$ term of a G.P. is m and $(p-q{)}^{th}$ term is n, then pth term will be _____.

• A. $mn$
• B. $\sqrt{mn}$
• C. $\left(\frac{m}{n}\right)$
• D. $(m-n)$

Answer 1

The correct option is B

$\sqrt{mn}$

Let $T_p$ be the $p^{th}$ term of G.P

$T_{p+q}=a{r}^{p+q-1}=m...\left(1\right)T_{p-q}=a{r}^{p-q-1}=n...\left(2\right)T_p=a{r}^{p-1}...\left(3\right)$

Multiplying (1) and (2)

$mn=a^2{r}^{2p-2}=(a{r}^{p-1}{)}^2$

$\Rightarrow T_p=a{r}^{p-1}=\sqrt{mn}$