Question

What is the average of the first n positive even numbers?

Answer 1

The average of all of them is the same as the average of the first and last, the same as the middle number in the group:
  1 + n

Answer 2

Solution:

we have been asked to find the average of the first n positive even numbers.

Let the firm n positive even numbers be

$2,4,6,8,10,12,.........2(n-1), 2n$

As we know that average of numbers$=\frac{\text{Sum of Numbers }}{Total number of Numbers}$

Required Average$=\frac{2+4+6+2(n-1)+2n}{n}$

Required Average$=\frac{2(1+2+3+....+(n-1)+n)}{n}$

As we know the sum of first n terms$=\frac{n(n+1)}{2}$

Required Average$=\frac{2n(n+1)}{2n}=n+1$