Question

If $(p+q{)}^{\text{th}}$ term of a G.P. is ${}^{\prime }{a}^{\prime }$ and its $(p-q{)}^{\text{th}}$ term is ${}^{\prime }{b}^{\prime }$ where $a,b\in R^{+}$, then its $p^{\text{th}}$ term is

• A. $\sqrt{\frac{a^3}{b}}$
• B. $\sqrt{\frac{b^3}{a}}$
• C. $\sqrt{ab}$
• D. None of these

Answer 1

The correct option is C $\sqrt{ab}$

Let ${}^{\prime }{A}^{\prime }$ be first term and ${}^{\prime }{r}^{\prime }$ be the common ratio.
We have,
$a=A{r}^{p+q-1},b=A{r}^{p-q-1}$
$\Rightarrow ab=A^2\times r^{2p-2}$
$\Rightarrow \sqrt{ab}=A{r}^{p-1}=p^{\text{th}}\text{term}$