A Progression

I found this out or figured it out by myself in early March of 2007:

If you add three consecutive numbers together, their sum goes up by increments of three.

Examples:
1+2=3
2+3=5
3+4=7
4+5=9
And so on.

I took that progression out a few numbers more but dropped it then.

When I came across it while I was going through some old notebooks, I thought I'd see if that was true for larger numbers.

So:
500+501+502=1503
501+502+503=1506.

I believe it goes on for infinity.

I'm sure there's some name for this, but I don't know what it is, since I'm more of an arts guy than a science/math guy.