I am having trouble with the following problem.

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> If $x\_1<x\_2$ are arbitrary real numbers and $x\_n = \frac{1}{3}x\_{n-1}+\frac{2}{3}x\_{n-2}$ for $n>2$, show that ${x\_n}$ (a sequence) is convergent.
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Notes: I know that the key to this problem is to show that ${x\_n}$ is a contractive sequence. If it is contractive I can prove it is convergent. But, I do not know how to prove it is contractive. Any help is appreciated.