"Sum of multiples of x from a to b" questions

GRE Quant Problem Solving
1

Hey all – been trying to get better at these “sum of multiples” questions. An examples being “what is the sum of the multiples of 5 from 1 - 100”

Can someone confirm that this approach is correct in the below fake problem?

Question: “What are the sum of multiples of 4 from 75 - 205, inclusive?”
Step 1: Find # terms = ((204-76)/4 +1) = 33 terms
Step 2: Find median = (204 + 76)/2 = median of 140
Step 3: Multply: terms and median = 4620

Is this right? I’ve tried double checking my work but can’t seem to find a good way to do so. Thanks!

2

All methods are the all the same , For Eg :

\frac{76}{4}=19 \ \\ \frac{204}{4}=51\

So, it become 4(19+20+21…+51) and 19 to 51 is 33 terms.
Again, we find the middle term of 19 to 51 → 35
So, 4 * (35 * 33) = 4620

3

to be fast we can use your result 76, 204, 33 terms without middle term
=33/2(76+204) = n/2(a+l) (AP)
=4260
am I right?