Q. A GP consists an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be equal to
A) 2
B) 3
C) 4
D) 5
Explanation
(c)
Let there be $2n$ terms in the given GP with first term $a$ and the common ratio $r$
According to the given condition
$a\frac{(r^{2n} - 1)}{(r - 1)} = 5a\frac{(r^{2n} - 1)}{(r^{2} - 1)}$
$\Rightarrow \ r + 1 = 5\ \Rightarrow r = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.