3 again

I love this number.
Find the sum of all the odd numbers between 10 and 550 that are divisible by three.
Answered July 28 by Mike Alexander Studied A-Level Mathematics, Physics & Computer Science
So, the odd numbers in the range go: [he shortens lists for visual reasons]
11 13 15 17 19 21 23 25 27 … 543 545 547 549
Every third number in bold is divisible by 3.
[Remember the math fact: if the sum of the digits in the number equals three, the number is divisible by three. Try it with each one of the boldface numbers.]
So, the sum is
15+21+27+33 … +543+549
Since all terms are divisible by 3, we can write this as:
3(5+7+9+11 … +181+183)
[Because multiplication is the inverse of division. Proof: multiply the last number, 183, by three, and the product is 549.]
Now notice that the series inside the parentheses is almost a full set of consecutive odd numbers - it just lacks 1+3+ at the start. So, it will be 4 less than the series:
I will stop here. If you want the rest of the proof, click https://www.quora.com/How-do-I-do-this-arithmetic-question-Find-the-sum-of-all-the-odd-numbers-between-10-and-550-that-are-divisible-by-3
The final answer is 25,380.
Guess what? The answer is divisible by three.