recursive formula


Definition of Recursive Formula

  • Recursive formula is a formula that is used to determine the next term of a sequence using one or more of the preceding terms.

Examples of Recursive Formula

  • The recursive formula for the sequence 5, 20, 80, 320, ... is an = 4 an-1.

Solved Example on Recursive Formula

The first term in a sequence is 39. Each term after the first term is 7 more than the term before it. Find the recursive formula for the sequence.
Choices:
A.
B. an = an-1 - 7, where a1 = 39
C. an =7 an-1 - 7, where a1 = 39
D. an = an-1 + 7, where a1 = 39
Correct Answer: D
Solution:
Step 1: a1 = 39                  [First term = 39.]
Step 2: a2 = a1 + 7 = 39 +7 = 46[Each term is 7 more than the term before it.]
Step 3: a3 = a2 + 7 = 46 + 7 = 53
Step 4: an = an-1 + 7                                 [This is a recursive formula.]
Step 5: The recursive formula for the sequence is an = an-1 + 7, where a1 = 39.

Related Terms for Recursive Formula

  • Term
  • Formula
  • Sequence