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Maths Sequence and Series ( Progressions ) NTA Abhiyas Question Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The consecutive odd integers whose sum is 45 2 - 21 2 are

43,45, ..... ,75

43,45,.....,79

43,45, ..... ,85

43,45, ..... ,89

Text Solution

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The correct answer is:

43,45, ..... ,89

Let n consecutive odd integers are

2m + 1,2m + 3,2m + 5,..... , 2m +2n - 1

Given that,

45 2 - 21 2 = (2m + 1) + (2m + 3) + (2m + 5)+ ......+ (2m + 2n - 1)

= 2mn + (1 + 3 + 5+..... + (2n - 1))

= 2mn + n 2

= m 2 + 2mn + n 2 – m 2

45 2 -21 2 = (m + n) 2 - m 2

m + n = 45 and m = 21

n = 24 and m = 21

Hence, the numbers are 43,45,..., 89

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