The average of odd numbers upto 100 is:

  Odd numbers up to 100 = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, .........., 99.

Sum =  1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 .................+ 99

Number of terms = \(\frac{first \; term \; + \; last \; term }{2}\)

n = \(\frac{1+99}{2}\)

= 50

The sum of odd numbers = n²

= 50²

= 2500

Average = \(\frac{50 × 50}{50}\)

= 50