Question

The sum of the terms of an infinite G.P. is 3 and sum of their square is also 3 then the first term and common ratio of the series is.

• A. $1,\frac{1}{2}$
• B. $\frac{3}{2},\frac{1}{2}$
• C. $\frac{1}{2},\frac{3}{2}$
• D. None of these

Answer 1

The correct option is B $\frac{3}{2},\frac{1}{2}$

Let the G.P be, $a,ar,a{r}^2,a{r}^3............\infty$ where $|r|<1$

Using given condition, $\frac{a}{1-r}=3..\left(1\right)$ and $\frac{a^2}{1-r^2}=\mathrm{3..}\left(2\right)$

Using operation $\left(2\right)/\left(1\right)$

$\frac{a}{1+r}=1\Rightarrow \frac{3(1-r)}{1+r}=1\Rightarrow r=\frac{1}{2}$

$\Rightarrow a=3(1-\frac{1}{2})=\frac{3}{2}$