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(52781) (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.

RELATED QUESTIONS
Good evening, I had a question regarding something that I could not find a topic for in... (answered by ikleyn)

Hello, I go to the Moring Star Online Homeschooling Academy. And need sever... (answered by scott8148)

Consider the sequence 8, 6, 3, �1, �6, ... a. Find the next two terms of the... (answered by stanbon)

How is doing operations (adding,subtracting,multiplying,and dividing) with rational... (answered by richard1234)

Hello, I need help finding the explicit formula for this problem. I'm fairly certain that (answered by math_helper)

Hello, Thanks in advance for your assistance. I need help with inequalities.... (answered by stanbon,rahman)

Hello, I need help with these proofs. I believe they are propositional logic and require... (answered by jim_thompson5910)

I need some refreshing. I have a problem figuring out some of the rules and properties of (answered by longjonsilver)

Hello I need help on some homework i do not understand its about number lines here is... (answered by checkley71)