Sum of certain consecutive odd positive intergers is `57^2 -13^2`
The least value of the an interger is

Options

A. 22
B. 27
C. 31
D. 43

Answer

B

Explanation

Let the odd integers be 2m+1,2m+3,2m+5,.. And let their number be n .Then,
`57^(2)-13^(2)=(n//2)[2(2m+1)+(n-1)xx2]`
`=n(2m+n)`
`=2mn+n^(2)`
`rArr(n+m)^(2)-m^2)=57^(2)-13^(2)`
`rArrm=13andn+m=57`
`rArrn=57-13=44`
Hence, the required odd integers are 27,29,31,.... 113.