Question

Mean of rirst n whole numbwrs

Answer 1

Answer:

In case of odd number of terms with same difference, the average will be the middle term.

In case of even number of terms with same difference, the average will be the average of two middle terms.

If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, then the combined average =.

If the average of n1 quantities is x and the average of n2 quantities out of them is y, the average of the remaining group =

The average of first n natural numbers = (n+1)/2

The average of squares of first n natural numbers = (n+1)(2n+1)/6

The average of cubes of first n natural numbers = n(n+1)2/4

The average of odd numbers from 1 to n = (last odd number+1)/2

The average of even numbers from 1 to n = (last even number+2)/2

The average of squares of first n odd numbers = (2n+1)(2n-1)/3

The average of first n odd numbers = n