Calculate the closed formula of a series We have the following series:
$$2, 1, 2, 1, 2, 1,...$$
and so on. 
Let $$x_0 = 2$$
Calculate the closed formula for $x_k$
The recursive formula for this series would be
$$x_k = x_{k−1} + x_{k−2} − {x_k−3}$$
How would I go about calculating the closed formula? Would be a division into cases, as in, if k is even x = 2, if k is odd, x = 1, be considered "closed"? This seems too easy to me. That is why I suspect "closed" might mean something else. 
Any hints would be appreciated.

Hint: Closed expression is something very very confusing, depends on the context. I would say that your solution is closed, but they probably mean that you have to consider your two cases together. Try to use what you know about the parity of $k$ using $(-1)^k.$ See what happens with the expression $1+(-1)^k$ for $k$ even and odd. Divide accordingly and add accordingly.
