Question

A geometric progression consists of 500 terms. Sum of the terms occupying the odd places when counting from the left is $P_1$ and the corresponding sum of the terms occupying the even places is $P_2$. Find the common ratio.

• A. $\frac{P_2}{P_1}$
• B. $\frac{P_1}{P_2}$
• C. $P_2+\frac{P_1}{P_1}$
• D. $P_2+\frac{P_1}{P_2}$

Answer 1

The correct option is A $\frac{P_2}{P_1}$

The answer would directly be $\frac{P_2}{P_1}$. Assume a series having a few number of terms e.g. 1, 2, 4, 8, 16, 32. The value of $P_2$ here = 42, while $P_1=21$. The common ratio can be seen to be $\frac{P_2}{P_1}=2$