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Math Example--Sequences and Series--Finding the Explicit Formula of an Arithmetic Sequence: Example 8

Finding the Explicit Formula of an Arithmetic Sequence: Example 8

Explicit Formula of Arithmetic Sequence Example 8

Topic

Sequences and Series

Description

Process for Finding the Explicit Formula

  1. Identify the First Term: The first term of the sequence is denoted as a1.
  2. Determine the Common Difference: The common difference d is found by subtracting the first term from the second term.
  3. Use the Explicit Formula: The nth term of an arithmetic sequence can be found using the formula:

an = a1 + d•( n − 1 )

       where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.

Given Sequence

Sequence: [25, 32, 39, 46, 53]

First term (a₁) = 25

Common difference (d) = 32 - 25 = 7

Explicit formula: an = 25 + (n - 1)7 = 7n + 18

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 arithmetic sequences, explicit formula