Multiple choice

Let $A$ be the sum of the first $20$ terms and $B$ be the sum of the first $40$ terms of the series $1^{2} + 2.2^{2} + 3^{2} + 2.4^{2} + 5^{2} + 2.6^{2} + .....$ If $B - 2A = 100\lambda$, then $\lambda$ is equal to

  1. $464$
  2. $496$
  3. $232$
  4. $248$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The series is 1^2, 2*2^2, 3^2, 2*4^2, 5^2, 2*6^2... The sum A (20 terms) and B (40 terms) can be calculated by grouping odd and even terms. The difference B - 2A simplifies to a known sum formula, yielding 24800, so lambda = 248.