MCQ practice · SSC General Mathematics Board questions · Chapter 13: Finite Series
What is the sum of the first n natural even numbers?
Think it through first, then pick an option.
- a n²
- b 2n² + 1
- c n² + n
- d 2n + 1
Answer and explanation
Correct answer: c n² + n
2 + 4 + ... + 2n = 2 × n(n + 1)/2 = n² + n.
Why the other options are wrong
- a n²: This is the sum of the first n odd numbers. The working is: 2 + 4 + ... + 2n = 2 × n(n + 1)/2 = n² + n.
- b 2n² + 1: This value does not come from applying the formula correctly. The working is: 2 + 4 + ... + 2n = 2 × n(n + 1)/2 = n² + n.
- d 2n + 1: This is a single odd term, not a sum. The working is: 2 + 4 + ... + 2n = 2 × n(n + 1)/2 = n² + n.
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