Question

The sum of infinite terms of a G.P. is x and on squaring the each term of it, the sum will be y, then the common ratio of this series is

• A. $\frac{x^2-y^2}{x^2+y^2}$
• B. $\frac{x^2+y^2}{x^2-y^2}$
• C. $\frac{x^2-y}{x^2+y}$
• D. $\frac{x^2+y}{x^2-y}$

Answer 1

The correct option is C $\frac{x^2-y}{x^2+y}$

We have $\frac{a}{1-r}=x$ ....(i)
and $\frac{a^2}{1-r^2}=\frac{a}{1-r}.\frac{a}{1+r}=y$ ....(ii)
$\Rightarrow y=x.\frac{a}{1+r}=x.\frac{x(1-r)}{1+r}\Rightarrow \frac{y}{x^2}=\frac{1-r}{1+r}$
$\Rightarrow \frac{x^2}{y}=\frac{1+r}{1-r}\Rightarrow \frac{x^2}{y}(1-r)=1+r$
$\Rightarrow r[1+\frac{x^2}{y}]=-1+\frac{x^2}{y}\Rightarrow r=\frac{x^2-y}{x^2+y}.$