Question

What is the sum of the first 10 terms of the sequence 1, 2, 4, 8, 16, ...?

• A. 1024
• B. 1023
• C. 1017
• D. 1026

Hint:

For powers of 2, the sum of terms up to $2^{n-1}$ is always $2^n - 1$.

Answer 1

The Correct Option is B

Step 1: Concept
This is a Geometric Progression (GP) where $a=1$ and the common ratio $r=2$.

Step 2: Meaning
The sum of $n$ terms of a GP is $S_n = a(r^n - 1) / (r - 1)$.

Step 3: Analysis
$S_{10} = 1(2^{10} - 1) / (2 - 1) = (1024 - 1) / 1$.

Step 4: Conclusion
$S_{10} = 1023$. Final Answer: (B)