Question

The sum of first $n$ terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of $n$ is

• A. 12
• B. 11
• C. 10
• D. 9
• E. 8

Hint:

Powers of 2 like $2^{10}=1024$ are frequently used in competitive math; memorizing them saves time.

Answer 1

The Correct Option is C

Step 1: Concept
The sum of the first $n$ terms of a G.P. is $S_n = \frac{a(r^n - 1)}{r - 1}$ for $r > 1$.

Step 2: Analysis
Given $S_n = 1023$, $a = 1$, and $r = 2$. $1023 = \frac{1(2^n - 1)}{2 - 1} \implies 1023 = 2^n - 1$.

Step 3: Calculation
$2^n = 1024$. Since $2^{10} = 1024$, we have $n = 10$. Final Answer: (C)