SOLUTION: Good evening, I had a question regarding something that I could not find a topic for in the options. I wanted to get some clarification on explicit and recursive rules. How do you

Algebra ->  Functions -> SOLUTION: Good evening, I had a question regarding something that I could not find a topic for in the options. I wanted to get some clarification on explicit and recursive rules. How do you       Log On


   

Question 1095381: Good evening, I had a question regarding something that I could not find a topic for in the options. I wanted to get some clarification on explicit and recursive rules. How do you find the explicit rule? How do you find the recursive rule?
Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Consider an arithmetic progression.

             I assume you know what it is.

    The recursive formula for the (n+1)-th term is  a%5Bn%2B1%5D = a%5Bn%5D%2Bd.

    It express the next term via the preceding one.


    The explicit formula for (n+1)-th term is a%5Bn%2B1%5D = a%5B1%5D%2Bn%2Ad.




2.  Similarly for an geometric progression.

             I assume you know what it is.

    The recursive formula for the (n+1)-th term is  a%5Bn%2B1%5D = a%5Bn%5D%2Ar.

    It express the next term via the preceding one.


    The explicit formula for (n+1)-th term is a%5Bn%2B1%5D = a%5B1%5D%2Ar%5En.


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On arithmetic progression see introductory lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.


On geometric progressions see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.