Question

Sum of certain consecutive odd positive integers is 57² – 13². Those integers are

• A. 27, 29,......, 113
• B. 25, 27, 29,....., 113
• C. 23, 25, 27,......, 113
• D. None of these

Answer 1

Answer: (A)

27, 29,......, 113

Answer 2

Let odd integers be 2m +1, 2m + 3,….. Let their number be n. then

57² – 13² = [2 (2m +1) + (n – 1). 2]

̃ 57² – 13² = 2mn + n²

̃ 57² – 13² = (m + n)² – m²

̃ m + n = 57

̃ n = 44

m = 13

so integers are 27, 29, 31,…… 113