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.
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