Here's one that might/might not be a bit of a challenge.
Construct a model of the periodic series
3, 6, 3, -3, -6, -3, 3, 6, 3, -3, -6, -3, 3, ...
I can construct a model for this, but the student that asked me the question also said that he was doing a unit on geometric and arithmetic series. My model doesn't even remotely resemble this approach. I can't see any way to apply two arithmetic series to this and get a periodic cycle, but is there a way to do this with two geometric series? I can't think of a way to approach this problem generally.
To be specific, could this somehow be something like
or some such?
(If you are curious I can post my solution. Just ask.)