The document describes a mathematical solution for calculating the sum of squares of numbers up to 312. It details a formulaic approach to derive the result using specific calculations, ultimately leading to the conclusion that the sum equals 5456. The final answer corresponds to choice (b) among multiple options.

1. Polynomials Q6

2. Qn: Sum of squares of nos.
(a) 9455 (b) 5456
(c) 3468 (d) 4892
What is the sum of 12 + 32 + 52 …….312?

3. Soln: Sum of squares of nos.
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 x 32 x 63
6
-
4 x 15 x 16 x 31
6
=
31 x 32 x 33
6
= 31 × 11 × 16 = 5456
Answer choice (b)
What is the sum of 12 + 32 + 52 …….312?