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

$\displaystyle c_n = a_0r^n + b_0p^n$

or some such?

Thanks!

-Dan

(If you are curious I can post my solution. Just ask.)