Question

the A.M of first n natural numbers is

Answer 1

A.M. = Sum of all terms/number of all terms

A.M. = (1+2+3+4+...........+n)/n

*Note: Sum of n natural number is (n(n+1))/2.

So, A.M. = n(n+1)/2n

Answer 2

First n natural numbers are 1,2,3,.....,n.

Now we have to find the arithmetic mean of first n natural numbers. we know that the sum of n natural number is n*(n+1)/2. [We can prove this by mathematical induction method.]

Then, A.M. = sum of first n natural numbers/n

                 = n*(n+1)/ 2n

                  =(n+1)/2

Answer: Arithmetic mean of first n natural number is (n+1)/2