Find the sum of all even numbers between 99 and 999.

Answer 1

To find the sum of all even numbers between 99 and 999, we need to list all the even numbers in this range and then add them up.

The first even number in this range is 100, and the last even number is 998.

We can notice that if we take the sum of the first and last even number and multiply it by half of the total number of even numbers, we will get the sum.

The total number of even numbers in this range can be calculated by dividing the difference between the first and the last number by 2 and adding 1.

First even number = 100
Last even number = 998

Total number of even numbers = (998 - 100)/2 + 1 = 450

Sum of the first and last even number = 100 + 998 = 1098

Sum of all even numbers between 99 and 999 = (Sum of the first and last even number) x (Total number of even numbers)/2 = 1098 x 450/2

= 549 x 450

= 247,500

Therefore, the sum of all even numbers between 99 and 999 is 247,500.