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CA Foundation · Quantitative Aptitude · Sequence and Series

What is the value of the sum of the first 15 natural numbers cubed, that is 1³ + 2³ + 3³ + ... + 15³?

The sum of cubes of the first n natural numbers equals the square of their sum. For n = 15 the sum is 120, so the required total is 120 squared, which is 14,400.

  1. A14,400Correct
  2. B12,100
  3. C1,240
  4. D3,600

Explanation

Sum of cubes of first n natural numbers = [n(n+1)/2]². For n = 15, n(n+1)/2 = 15×16/2 = 120, so the sum is 120² = 14,400. The option 1,240 is wrong because it wrongly gives the sum of the first 15 natural numbers squared (1,240) rather than cubed. The value 120 itself is just the sum of the natural numbers.

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