defined recursively

Question

Question: A sequence is defined recursively by

$$ \left\{ \begin{array}{ccc} a_{n+2} &=& 2a_{n+1} - a_n \\ a_0 &=& 2 \\ a_1 &=& 1 \end{array} \right. $$

Find $a_4$ Anyone know how to do this? This is what I've done I'm not sure if its correct. $a_2 = 2a_2+1 - 2 = 1$

$ a_3 = 2a_3+1 - 3 = 1$

$ a_4 = 2a_4+1 - 4 = 4$

Answer 1

Just do them one after another.

$a_{n+2} = 2a_{n+1} -a_n$.

So $a_2 = 2a_1 - a_0 = 2*1 - 2 = 0$

And $a_3 = 2a_2 - a_1 = 2*0 - 1 = -1$

So $a_4 = ????$