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# 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 = 4an-1.

### 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. an = a(n-1) / 7 where a1 = 39
• B. aan = a(n-1) - 7, where a1 = 39
• C. aan =7a(n-1) - 7, where a1 = 39
• D. aan = a(n-1) + 7, where a1 = 39

#### 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.

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