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.