Question

Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is
[AIEEE 2002]

• A. 5
• B. 3/5
• C. 8/5
• D. 1/5

Answer 1

The correct option is B

3/5

$\frac{a}{1-r}=20$ ......... (i)
$\frac{a^2}{1-r^2}=100$ ......... (ii)
From (i) and (ii),
$\frac{a}{1+r}=5,$ [$\because$ a = 20(1 - r) by (i)]
$\Rightarrow \frac{20(1-r)}{1+r}=5\Rightarrow 5r=3\Rightarrow r=3/5.$