Finding the Explicit Formula of an 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 a_1.
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:

a_n = a₁ + d•( n − 1 )

       where a_n 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: a_n = 25 + (n - 1)7 = 7n + 18

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