I am self-learning Discrete Mathematics and I am supposed to solve the following Exercise. (Translated from Portuguese).
The sequence $(a_{n})$ is defined by $a_{1}=1, a_{2}=2,a_{n+1}=a_{n}-a_{n-1},$ if $n\gt 2$. Prove that $a_{n+6}=a_{n}$ for all natural numbers $n.$ Describe all terms of this sequence.
I think I didn't understand the last sentence, because I thought that $a_{n+6}=a_{n}$ is the description of all terms of this sequence. But as you can see, I am wrong!
Here is the sequence $(1,2,1,-1,-2,-1,1,2,1,-1,-2,-1,\cdots).$ Should I find a formula for the terms of the sequence?