Question

Sum of certain odd consecutive positive integers is 57² –13² , then the integers are

(a)  25, 27, 29,..........111

(b)  27, 29, ..............113

(c)  29, 31, 33,...........115

(d)  None of these

Answer 1

Correct option  (b) 27, 29, ..............113 

Explanation:

(2m + 1) + (2m + 3) +..............n terms = 57² – 13² 

n/2 {2.(2m + 1) + (n – 1)2} = 57² – 13² 

n(2m + n) = 57² – 13² 

n² + 2mn + m²–m² = 57² – 13² 

(n + m)²–m² = 57² – 13² 

n + m = 57 and m = 13, Solve to get n = 44

Hence, the series is

27, 29, 31,.......................,113