Question

The sum of an infinite number of terms of a G.P. is $20$, and the sum of their squares is $100$, then the first term of the G.P. is

• A. $5$
• B. $\frac{8}{5}$
• C. $\frac{3}{5}$
• D. $8$

Answer 1

The correct option is D $8$

By formula for summation over infinite terms of a GP,
$\frac{a}{1-r}=20$

$\frac{a^2}{1-r^2}=100$

$\frac{a}{1-r}.\frac{a}{1+r}=100$

$\frac{a}{1+r}=5$

$a=5+5r;a=20-20r$

$r=3/5⟹a=8$