Determine the sum of all multiples of $4$ between $1$ and $999$

Question

Determine the sum of all multiples of $4$ between $1$ and $999$.

These types of questions weren't covered in class, and I'm not sure how to proceed.

We're learning about arithmetic and Geometric sequences and series.

I think I should use the formula $S_n=\frac{n}{2}(2a+(n-1)d).$

I think $d=4$ and $a=1$?

Answer 1

$4+8+...+996=4(1+2+...+249)$. I think you can continue from here.

Answer 2

Another way to do is like what Gauss did at his class $4 + 8 + \cdots + 996 \\ = (4 + 996) + (8 + 992) + \cdots + (496 + 504) + 500 \\ = 1000 \times \dfrac{496}{4} + 500 \\ = 124,500$