Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
Try writing out a few terms and thinking about a formula that might fit the results. – Gerry Myerson Jul 9 '12 at 7:29
This answer illustrates a technique that will work for problems of this kind. – Brian M. Scott Jul 9 '12 at 7:46
up vote 2 down vote accepted

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 $$a_n=a_{n-1}+5=(a_{n-2}+5)+5=a_{n-2}+10=(a_{n-3}+5)+10=a_{n-3}+15=$$$$...=a_1+5(n-1)$$

share|cite|improve this answer
Not leaving much for OP to do. – Gerry Myerson Jul 9 '12 at 7:45

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.