Question

Add the even numbers between 1 and 100

Answer 1

The sum of even numbers between 1 and 100 is 2550.

Explanation:

To find : Add the even numbers between 1 and 100?

Solution :

The even numbers from 1 to 100 is 2,4,6,...,100 form an arithmetic progression,

The first term is a=2

The common difference is d=2

The last term is l=100

First we find the number of terms given by,

`l=a+(n-1)d`

`100=2+(n-1)2`

`100=2+2n-2`

`2n=100`

`n=(100)/(2)`

`n=50`

The sum formula of A.P is

`S_n=(n)/(2)[a+l]`

Substitute the values in the formula,

`S_(50)=(50)/(2)[2+100]`

`S_(50)=25* 102`

`S_(50)=2550`

Therefore, The sum of even numbers between 1 and 100 is 2550.