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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.


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

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