Q. An infinite GP has first term $x$ and sum 5, then $x$ belongs to
A) $x < - 10$
B) $- 10 < x < 0$
C) $0 < x < 10$
D) $x > 10$
Explanation
(c)
Let $r$ be the common ratio of give GP.
$\therefore\ \frac{x}{1 - r} = 5$
$\Rightarrow \ r = \left( 1 - \frac{x}{5} \right)$
$\because\$ For infinite GP,
$|r| < \ 1$
$\Rightarrow \ - 1 < 1 - \frac{x}{5} < 1$
$\Rightarrow \ \ 10 > x > 0$
$\Rightarrow \ 0 < x < 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.