Here is an explanation of the rainbow method.
The idea is as follows:
You can add a series of consecutive numbers (means the difference is the same:
like 2+4+6+...100 (difference 3) or
5+ 10 + 15 +....+1000 (difference 5) etc. by making bows where each bow consists of two numbers: first + last, then second + one before the last etc.
Thus all you need to do is to multiply that sum (first+last) times the numbers of bows which is half of the number of numbers.
3+6+9+12+15 has 2.5 bows and each bow equals 18 so the answer is 45 (you can verify)
or another example:
15+25+35+....1005 has 100 bows and each bow has the same sum of 1020 so the answer is 102,000
Remark. It is good if you play with small lists to practice the method. Like 2+4+6+8+10 or 5+10+15+20+25+30 to get the "feel"