Question

What is the sum of all possible multiples of 5 less than 500

Answer 1

Answer:

We need to find 5 + 10 + 15 + ... + 485 + 490 + 495. There are 99 numbers that are being added. To add this we can do 5 + 495, 10 + 490, 15 + 485 and so on. These pairs have a sum of 500 and since there are 98 / 2 = 49 pairs their sum is 500 * 49 = 24500. Since there is an odd number of numbers that are being added, there is one number that does not belong to a pair. That number is the 50th number in the list which is 50 * 5 = 250. Therefore the answer is 24500 + 250 = 24750.