RECURRING DECIMAL
Definition of Recurring Decimal
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_{n1}
Video Examples: Recurring Decimals
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_{n1} /7, where a_{1} = 39B. a_{n} = a_{n1}  7, where a_{1} = 39
C. a_{n} = 7 a_{n1}  7, where a_{1} = 39
D. a_{n} = a_{n1} + 7, where a_{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_{n} = a_{n1} + 7 [This is a recursive formula.]
Step 5: The recursive formula for the sequence is a_{n} = a_{n1} + 7, where a_{1} = 39.
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