# Finding the Explicit Formula of an Arithmetic Sequence: Example 5

## 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: [4, 9, 14, 19, 24]

First term (a₁) = 4

Common difference (d) = 9 - 4 = 5

Explicit formula: an = 4 + (n - 1)5 = 5n - 1

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Common Core Standards CCSS.MATH.CONTENT.HSF.BF.A.2 9 - 11 Algebra     • Sequences and Series         • Sequences 2022 arithmetic sequences, explicit formula