Q. An infinite GP has first term $x$ and sum 5, then
A) $x < - 10$
B) $- 10 < x < 0$
C) $0 < x < 10$
D) $x > 10$
Explanation
(c)
Since, $S_{\infty} = \frac{x}{1 - r} = 5\ \ \ \ \ \ \ \Rightarrow r = \frac{5 - x}{x}$ [thus $|r| < 1\rbrack$
$\Rightarrow - 1 < \frac{5 - x}{5} < 1\ \ \ \Rightarrow \ 0 < x < 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.