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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.

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    [This answer](http://math.stackexchange.com/a/144335/12042) illustrates a technique that will work for problems of this kind.2012-07-09

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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)$

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    Not leaving much for OP to do.2012-07-09