The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______. A. n^2 = n B. n^2 + n C. 2n^2 = n D. 2n^2 + n

GATE 2020 · General Aptitude · Arithmetic Series · medium

Answer: The difference is n^2 + n. Answer: B. n^2 + n.

1. Sum of first 2n natural numbers: With m = 2n: S(2n) = 2n(2n+1)/2 = n(2n+1) = 2n^2 + n.
2. Sum of first n odd natural numbers: S_odd(n) = n^2. (These n terms form an AP with first term 1, last term 2n-1, so sum = n*(1 + (2n-1))/2 = n^2.)
3. Compute the difference: D = (2n^2 + n) - n^2 = n^2 + n.