SOLUTION: Hello. I needed some help with explicit and recursive rules. I do not understand how to write one of these rules when asked to on a worksheet. If you can, please describe this to m

Question 1095389: Hello. I needed some help with explicit and recursive rules. I do not understand how to write one of these rules when asked to on a worksheet. If you can, please describe this to me step by step. (I just started Algebra I)
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.
The recursive formula usually expresses the current term via the preceding one.

So, the recursive formula for the current term refers to the preceding term.

In opposite, the explicit formula expresses the current term directly, without the reference to the preceding term.

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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