## Related Words

# 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} = 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. an = a
_{(n-1)}- 7, where a_{1}= 39 - C. an =7a
_{(n-1)}- 7, where a_{1}= 39 - D. an = 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.

Translate :