let $a\_1=1$, $a\_2=2$, and define $a\_n=\frac{1}{2}(a\_{n-1}+a\_{n-2})$. How can I show that this sequence is Cauchy?

I began with $|a\_n-a\_{n-1}|=\frac{1}{2}(a\_n-a\_{n-1})$

which goes to $\frac{1}{2}(a\_{n-1}+a\_{n-2})-\frac{1}{2}(a\_{n-2}+a\_{n-3})$

I am have been toying with this for quite some time and it is just not clicking. Can somebody please help!