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Math Example--Sequences and Series--Finding the Explicit Formula of a Geometric Sequence: Example 1

Finding the Explicit Formula of a Geometric Sequence: Example 1

Explicit Formula of Geometric Sequence Example 1

Topic

Sequences and Series

Description

Methodology for Finding the Explicit 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 Explicit Formula: The nth term of a geometric sequence can be found using the formula:

an = a1•r(n - 1)

       where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Given Sequence

Sequence: [3, 6, 12, 24, 48]

First term (a₁) = 3

Common ratio (r) = 6 / 3 = 2

Explicit formula: an = 3•2(n - 1)

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, explicit formula