Question

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

Answer 1

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
`=(2+4+6+2(n-1)+2n)/(n)\\`

Required Average
`=(2(1+2+3+....+(n-1)+n))/(n)`

As we know the sum of first n terms
`=(n(n+1))/(2)`

Required Average
`=(2n(n+1))/(2n)=n+1 \\`

Answer 2

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