CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Sum of squares of nos.

The question is about Sum of squares of nos. There is a formula for adding the squares of N natural numbers. What about sum of squares of N odd numbers? 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 4: What is the sum of 12 + 32 + 52 …….312?

  1. 9455
  2. 5456
  3. 3468
  4. 4892

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: Use the formula for sum of squares of numbers !!

This Expression is same as (12 + 22 + 32 + 42 + 52 …….302 + 312) – (22 + 42 + 62 ….302)

= (12 + 22 + 32 + 42 + 52 …….302 + 312) – 4(12+ 22 + 32 ….152)

12 + 22 + 32 +.......... + n2 = (n(n+1)(2n+1))/6, for all n > 1.

Expresssion = (31 * 32 * 63)/6 - (4 * 15 * 16 * 31)/6
= (31 * 32 * 33)/6 = 31 * 11 * 16 = 5456

The question is "What is the sum of 12 + 32 + 52 …….312?"

Hence the answer is "5456"

Choice B is the correct answer.

 


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