About Recursive Formula
Let's review what a recursive function is before learning the recursive formula. A recursive function is one that defines each term of a series using a previously known term, i.e. one in which the next term is dependent on one or more previously known terms (s). h(x) is a recursive function that can be written as follows:
h(x) = a0h(0) + a1h(1) + ....... + ax-1h(x-1) ; ai≥ 0 and at least one of the ai> 0
A recursive formula is one which uses the prior phrase to define each term in a sequence (s). The following parameters are defined using the recursive formulas:
- The first term of sequence
- The pattern rule to get any term from its previous term
Recursive Formulas
The recursive formulas for various types of sequences are listed below..
Recursive Formula for Arithmetic Sequence
To find nth term of an arithmetic series, use the recursive formula:
an= an-1+ d for n ≥ 2
where
- anis the nthterm of a A.P.
- d is the common difference.
Recursive Formula for Geometric Sequence
To find nth term of a geometric series, use the recursive formula:
an= an-1r for n ≥ 2
where
- anis the nthterm of a G.P.
- r is the common ratio.
Recursive Formula for Fibonacci Sequence
To find the nth term of a Fibonacci sequence, use the recursive formula:
an= an-1+ an-2for n ≥ 2, where
- a0= 1 and
- a1= 1
where anis the nthterm of the sequence.
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