In the set of positive integers from 1 to 500, what is the sum of all the odd multiples of 5?

Odd multiples of 5 are in the sequence:
5, 15, 25, 35..........n with a common difference of 10
There are 500/5 = 100 multiples of 5 from 1 to 500 in which half are odd and half are even. Hence there are 50 odd multiples from 1 to 500

Therefore, the sequence of odd multiples of 5 from 1 to 500 =>
5, 15, 25, 35, 45, 55..................495
Where d = 10, a = 5, l = 495, and n = 50
$$Sum\ of\ all\ the\ 50\ terms\ =\frac{n\left(a+l\right)}{2}$$
$$=\frac{50\left(5+495\right)}{2}=25\cdot500$$
$$=12,500$$

Answer = B