Question

If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are
[RPET 1999]

• A. 3/2, 1/2
• B. 1, 1/2
• C. 3/2, 2
• D. None of these

Answer 1

The correct option is A

3/2, 1/2

$\frac{a}{1-r}=3$ …..(i) and $\frac{a^2}{1-r^2}=3$ .....(ii)
From (i) and (ii), $\frac{a}{1+r}=1$
From (i), $\frac{1+r}{1-r}=3\Rightarrow r=\frac{1}{2},$ from (i), a = 3/2
So, first term = 3/2 and common ratio = 1/2.