The problem requires solving a problem by calculating Z-transform from the following:
a(n)=cos(2n+1)
I'm not really a maths person myself, so I can't assess the difficulty of the question, but he says it's much more complex than problems normally solved during the classes.
If you wanted a closed form representation of the Z transform you could use the complex exponential representation of cosine, at which point you get two geometric series.

Of course you might not need a closed form representation