Question

What is the sum of the multiples of 3 between 3 and 999, inclusive?

Answer 1

The sum is `166,833`.

Explanation:

We note that each multiple of `3` is `3` apart from the next multiple of `3`. This will serve as our common difference, `d`. We know that our nth term is `999`. Let's find the value of `n`.

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

`999 = 3 + (n - 1)3`

`999 = 3 + 3n - 3`

`999 = 3n`

`n = 333`

We can now use the formula `s_n = n/2(2a + (n - 1)d))` to determine the sum.

`s_333 = 333/2(2(3) + (333 - 1)3)`

`s_333 = 333/2(1002)`

`s_333 = 166,833`

Hopefully this helps!