**Solution:**

The odd numbers between 0 and 50 are 1, 3, 5, 7, 9 … 49.

Therefore, we can see that these odd numbers are in the form of AP.

Hence,

First term, a = 1

Common difference, d = 2

Last term, l = 49

By the formula of last term, we know,

l = a + (n − 1) d

49 = 1 + (n − 1)2

48 = 2(n − 1)

n − 1 = 24

n = 25 = Number of terms

The sum of n terms of an AP is:

S_{n} = n /2( a + l )

S_{25} = 25/2 (1 + 49)

= 25(50)/2

= (25)(25)

= 625