The odd numbers between 0 and 50 are

1,3,5,................49

Total number of terms n = 25

It forms an arithmetic series. 

Now

first term a = 1

common difference d = 2

Now sum of first 15 terms of AP = (n/2) *{2a + (n-1)*d}

                                               = (25/2)*{2*1 + (25-1)*2}

                                               = (25/2)*(2 + 24*2)

                                               = (25/2)*(2 + 48)

                                               = (25*50)/2

                                               = 25*25                   (when 50 and 2 is divided by 2)

                                               = 625

So sum of odd numbers between 0 and 50 = 625