Question

If $S_n$ stands for the sum to $n$-terms of a G.P. with $a$ as the first term and $r$ as the common ratio, then $\frac{S_1}{S_2}$ is:

• A. $r^n + 1$
• B. $1/r^n + 1$
• C. $r^n - 1$
• D. $\frac{1}{r^n - 1}$

Answer 1

The Correct Option is B

The sum of the first term $S_1 = a$.

For two terms, $S_2 = a(1 + r)$. Then: $\frac{S_1}{S_2} = \frac{a}{a(1 + r)} = \frac{1}{r + 1}$. 

Hence, $\frac{1}{r + 1}$ is the required result.