Question

What is the sum of all integers that are multiples of 4 from 1 to 150? *Show your solution*

Answer 1

There's a pretty simple formula to follow: count of multiples
`*` average of the multiple.

To find the average, we take the smallest multiple of 4 which is in the range of 1 and 150 which is 4 of course. And the largest would be 148 since that's the only number in the range. So now average them:
`(4 + 148)/(2) = (152)/(2) = 76`

Now we find the count of the multiples which is in the range of 1 to 150. To do that, we use this formula:

`\frac{\text{largest multiple} - \text{smallest multiple}}{n} \\`

Here,
`n` is 4 so this would be:

`(148-4)/(4) = (144)/(4) = 36`

This would give you the exclusive count of all the numbers, but we want the inclusive count so, we simple add 1 so the count would be
`37`

Now following the 1st formula we get:
`37 * 76 = 2812`

So the answer would be 2812! :D

And here's the check too: