Question

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

• A. $nm$
• B. $\sqrt{nm}$
• C. $\frac{m}{n}$
• D. $\sqrt{\frac{m}{n}}$

Answer 1

The correct option is B $\sqrt{nm}$

Let the first term of G.P be 'a' and common ratio be 'r'
given $T_{p+q}=a{r}^{p+q-1}=m{T}_{p-q}=a{r}^{p-q-1}=n$
then multiplying the above two equations :
$mn=a^2{r}^{2p-2}={\left(a{r}^{p-1}\right)}^2\Rightarrow a{r}^{p-1}=\sqrt{mn}$
but $a{r}^{p-1}$ is the $p_{th}$ term of the G.P
hence $T_p=\sqrt{mn}$