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} = 4a_{n-1}.

Video Examples: Recursive Formula

Solved Example on Recursive Formula

Ques: 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. a_{n }= a_{(n-1)} / 7 where a_{1} = 39
B. aa_{n }= a_{(n-1)} - 7, where a_{1} = 39
C. aa_{n }=7a_{(n-1)} - 7, where a_{1} = 39
D. aa_{n }= a_{(n-1)} + 7, where a_{1} = 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 = a_{(n-1)} + 7 [This is a recursive formula.]
Step 5: The recursive formula for the sequence is an = a_{(n-1)} + 7, where a1 = 39.