We know that mean or average of observations, is the sum of the values of all the observations divided by the total number of observations.

and, we have first n odd natural numbers as

1, 3, …, 2n - 1

Clearly the above series is an AP(Arithmetic progression) with

first term, a = 1 and

common difference, d = 2

And no of terms is clearly n.

And last term is (2n - 1)

We know, sum of terms of an AP if first and last terms are known is:

Putting the values in above equation we have sum of series i.e.

…[1]

As,

Mean

⇒ Mean