I know how to get the explicit formula for homogeneous successions, kinda. What I do is get the characteristic equation, get the solutions and then solve a system to obtain the values of A,B,C... constants to build the explicit formula.
... But what if the succession is heterogeneous? Particularly, this question:
Determine the explicit formula for the succession defined by recurrence by $a_n=a_{n-1}+5$ with $a_1=3$
Which, apparently, is heterogeneous.