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 a_n = 4 a_n-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. a_n = a_n-1 - 7, where a₁ = 39
C. a_n =7 a_n-1 - 7, where a₁ = 39
D. a_n = a_n-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: a_n = a_n-1 + 7                                 [This is a recursive formula.]
Step 5: The recursive formula for the sequence is a_n = a_n-1 + 7, where a₁ = 39.

Related Terms for Recursive Formula

• Term
• Formula
• Sequence

Additional Links for Recursive Formula

• Click here for samples
• Back to Mathematics Dictionary