Question 478068
The number of odd integers from 25 to 99:

99 = 25 + (n-1)2 ==> 74 = (n-1)2 ==> 37 = n-1 ==> n = 38

==> {{{S[o] = (38/2)(25 + 99) = 19*124 = 2356}}}

The number of even integers from 26 to 100:

100 = 26 + (n-1)2 ==> 74 = (n-1)2 ==> 37 = n-1 ==> n = 38

==> {{{S[e] = (38/2)(26 + 100) = 19*126 = 2394}}}

==> {{{S[e] - S[o] = 2394 - 2356 = 38}}}.