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Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 7

Finding the Recursive Formula of a Geometric Sequence: Example 7

Recursive Formula of Geometric Sequence Example 7

Topic

Sequences and Series

Description

Process for Finding the Recursive Formula

  1. Identify the First Term: The first term of the sequence is denoted as a1.
  2. Determine the Common Ratio: The common ratio r is found by dividing the second term by the first term.
  3. Write the Recursive Formula: The recursive formula for an arithmetic sequence is:

an = an - 1•r

       where an is the nth term, an - 1 is the previous term, and r is the common ratio.

Distinguishing Recursive from Explicit Formulas

  1. Recursive Formula: Defines each term based on the previous term(s). It requires knowing the initial term and is useful for generating terms sequentially.
  2. Explicit Formula: Allows direct computation of any term in the sequence without reference to previous terms. It is more efficient for finding terms far into the sequence.

Given Sequence

Sequence: [2, 10, 50, 250, 1250]

First term (a₁) = 2

Common ratio (r) = 10 / 2 = 5

Recursive formula: an = an - 1•5

For a complete collection of math examples related to Sequences and Series click on this link: Math Examples: Sequences and Series Collection.

Common Core Standards CCSS.MATH.CONTENT.HSF.BF.A.2
Grade Range 9 - 11
Curriculum Nodes Algebra
    • Sequences and Series
        • Sequences
Copyright Year 2022
Keywords geometric sequence, recursive formula