Sorry if this is a duplicate or easy (a lot of the other 'how do i solve recursive equation' questions were for more complex equations). How can I solve this for arbitrary $F\_n$ with arbitrary constants $c\_1$ and $c\_2$.

$$F\_{n+1} = F\_{n} \cdot c\_1 + c\_2$$

Also does it matter if $c\_1$ and $c\_2$ are constants or would it work if they were functions themselves such as:

$$F\_{n+1} = F\_{n} \cdot g + h$$