Question

Find the sum of series 1^2+3^2+5^2+…………………………..+11^2.

(a) 279

(b) 286

(c) 309

(d) 409

The question was asked in final exam.

This intriguing question comes from Sum to n Terms of Special Series in division Sequences and Series of Mathematics – Class 11

Answer 1

Right choice is (b) 286

Explanation: 1^2+3^2+5^2+…………………………..+11^2

= (1^2+2^2+3^2+……+11^2) – (2^2+4^2+6^2+8^2+10^2)

= (1^2+2^2+3^2+……11^2) – 2^2(1^2+2^2+3^2+4^2+5^2)

= 11*12*23/6 – 4*5*6*11/6

= 506 – 220

= 286.