Question

The sum of an infinite G.P. is 23 and the sum of squares of the series is 69, then first term is :

• A. 69/2
• B. 10/3
• C. 9/10
• D. 13/69

Answer 1

The correct option is A

69/2

$\frac{a}{1-r}$ = 23, $\frac{a^2}{1-r^2}$ = 69 ⇒ $\frac{a}{1+r}$ = $\frac{69}{23}$ ⇒ r = - $\frac{1}{2}$ ⇒ a = $\frac{69}{2}$