Hey guys! I got challenged by my teacher to do a certain problem for extra credit... i'm past the date to submit it anyway but it's completely wrecking my brain. Since we're studying arithmetic and geometric sequences, and their sums, I believe that we're supposed to use them. Here's the problem:

A person is out for a walk. He takes 1 step to his right, then turns right and takes 2 steps, then turns right and takes 3 steps, then turns right and takes 4 steps, then turns right and takes 5 steps, etc. After he has taken a total of 2000 steps he receives a phone call that tells him to return. Instead of retracing his steps, he returns in a straight line to his starting point. How many steps will he require?

I've tried to approach this problem in many ways. I'm going to try to scan my work in for you guys to see since I did it in paper, but I'll take a while since I'll have to scan it in and edit the mess.

Also, a note: I believe the doesn't get to the 2000 steps, since 2000 would be between the 62nd and 63rd iterations I believe (from my own calculations) - but it is accepted to stop after the 62nd iteration, at step 1953 I believe.

Thanks!