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Question 918754: Please explain what recursive and explicit formulas in algebra are. Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a recursive formula works off the previous number in the sequence.
an explicit formula derives a number in the sequence based on a formula that doesn't depend on knowing the previous number.
for example:
An = An-1 + 4 is a recursive formula.
you would start with a known number, like A1 = 5
then each succeeding number would depend on the value of the preceding number.
A2 = A1 + 4
A3 = A2 + 4
A4 = A3 + 4
if A1 = 5, then A2 = 9 and A3 = 13 and A4 = 17, etc.
If you wanted to know the value of A10, you would need to know the value of A9.
You might be able to figure out what A10 would be directly, but it wouldn't be easy and would require you to do some thinking or creating a new formula to figure it out.
An explicit formula allows you to find the number in a sequence without having to know the previous number.
for example:
An = A1 + (n-1)d
Once you know A1 and d, you can figure out the value of A10 directly.
If A1 = 5 and d = 4, A4 would be equal to 5 + 3*4 = 5 + 12 = 17
A10 would be equal to 5 + 9*4 = 5 + 36 = 41.
The whole sequence up to A10 is:
5
9
13
17
21
25
29
33
37
41
in algebra, these formulas are usually defined in reference to sequences.
here's a tutorial and some exercises that talks about recursive and explicit formulas when referencing sequences.
http://www.algebralab.org/lessons/lesson.aspx?file=algebra_arithseq.xml
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