Find the first Frobenius series solution with nonzero positive exponent (when $r=1$) of singularity up to four nonzero terms

Question

The differential equation is $(x-2)y"+2xy=0$ with singular point $x = 2$.

I'm all good until I got stuck at the recurrence relation part where i have an, an-1 and an-2 .. appreciate if someone can provide some hints for this question as it's quite lengthy