CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Summation

The question is about sum of a series. We need to find out the sum of the series after simplifying the series. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 12: 6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to?

  1. 3680
  2. 4290
  3. 5720
  4. 6170

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: How you would simplify this series?

= 1 * 2 * 3 + 2 * 3 * 4 + 3 * 4 * 5 + 4 * 5 * 6 + 5 * 6 * 7....
= n (n + 1) (n + 2)
Or, (m – 1) m (m + 1) where m = n + 1
= m3 – m
Sum of all these = \\frac{(m(m+1))^2}{2^2}\\) - \\frac{(m(m+1))}{2}\\) = \\frac{(m(m+1))}{2}\\) * \\frac{(m(m+1))}{2}\\) - 1)
= \\frac{(m(m+1)(m^2+m+1))}{4}\\)
Substituting m = n + 1, we get
=\\frac{((n+1)(n+2)((n+1)^2+n+1-2))}{4}\\)
=\\frac{((n+1)(n+2)(n^2+2n+1+n+1-2))}{4}\\)
=\\frac{((n+1)(n+2)(n^2+3n))}{4}\\)
=\\frac{((n+1)(n+2)(n)(n+3)))}{4}\\)
=\\frac{(n(n+1)(n+2)(n+3))}{4}\\) . ….. Surprisingly enough, this seems to work!!!
Substituting n = 10,
We get \\frac{(10(11)(12)(13))}{4}\\) .
= 10 * 11 * 3 * 13 = 4290

The question is "6 + 24 + 60 + 120 + 210 + 336 + 504 + 720…. upto 10 terms is equal to?"

Hence the answer is "4290"

Choice B is the correct answer.

 


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