CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about sum of a sequence. A series in a different form is given and we need to find out the sum of it. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 14: Find sum of 2 ² + 2 * 3² + 3 * 4² + 4 * 5².....10 * 11²?

1. 6530
2. 3600
3. 2850
4. 3850

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: What is the form of the series?

The series is in the form n(n + 1)² = n³ + 2n² + n

Then Σ n³ + 2n² + n = [\\frac{n(n + 1)}{2}\\) ]² + 2 [n (n + 1)\\frac{2n + 1)}{6}\\)] + [\\frac{n(n + 1)}{2}\\)]
Substituting n = 10 will give the sum of the series. Thus Σ [\\frac{10 * 11)}{2}\\)]² + [\\frac{10 * 11 * 21)}{6}\\) ] + [\\frac{10 * 11)}{2}\\)]

The question is "Find sum of 2 ² + 2 * 3² + 3 * 4² + 4 * 5².....10 * 11²?"

Hence the answer is "3850"

Choice D is the correct answer.