**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, wherea_{1}= 39

C.a_{n}=7a_{n-1}- 7, wherea_{1}= 39

D.a_{n}=a_{n-1}+ 7, wherea_{1}= 39

Correct Answer: D

Solution:

Step 1:a_{1}= 39 [First term = 39.]

Step 2:a_{2}=a_{1}+ 7 = 39 +7 = 46[Each term is 7 more than the term before it.]

Step 3:a_{3}= a_{2}+ 7 = 46 + 7 = 53

Step 4:a[This is a recursive formula.]_{n}= a_{n-1}+ 7

Step 5:The recursive formula for the sequence isa_{n}=a_{n-1}+ 7, wherea_{1}= 39.

**Related Terms for Recursive Formula**

- Term
- Formula
- Sequence