Question

The mean of first n odd natural number is​

Answer 1

hola

mean = sum of observation / no of observation

= 1

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Answer 2

Mean of first n odd numbers is n.

Odd number starts from 1 .

The series of odd numbers is 1 , 3 , 5 , 7, 9 , and so on.

We have to find the mean of first n odd numbers.

To obtain the mean of n numbers, we find the sum of n numbers and then divide the sum by n.

Now to find the sum of n odd numbers , we see that the given odd numbers are in AP with first term(a) = 1 and common difference(d) = 2.

Applying the formula of sum of n terms of AP,

Sum of n terms of AP =

Substituting the value of a and d in the equation, we get

Now calculating mean of n odd number,

Dividing the sum by n, we get

Mean of n odd numbers = = = n.