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

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(52797) (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   = .

    It express the next term via the preceding one.


    The explicit formula for (n+1)-th term is  = .




2.  Similarly for an geometric progression.

             I assume you know what it is.

    The recursive formula for the (n+1)-th term is   = .

    It express the next term via the preceding one.


    The explicit formula for (n+1)-th term is  = .

------------
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.

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