particular solution for non-homogeneous equation

hello, i just started learning about this and i'm a little bit confused on how to find the particular solution for these 2 non-homogeneous equations.

$\displaystyle S_n = S_{(n-1)}+2n$ and $\displaystyle g_{n} = 5g_{(n-1)} - 6g_{(n-2)} + n + 5$

I know how to find a particular solution for an equation like $\displaystyle g_{n} = g_{(n-1)} - 2g_{(n-2)} + 2$ which is -1, but when there is a variable n instead of just a constant at the end, i get confused.

can someone help me get started? thanks!