Solving heterogeneous successions 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.

If you have that $a_n=a_{n-1}+5$, with $a_1=3$, then you have that $a_n=5(n-1)+3$, because $$a_n=a_{n-1}+5=(a_{n-2}+5)+5=a_{n-2}+10=(a_{n-3}+5)+10=a_{n-3}+15=$$$$...=a_1+5(n-1)$$