Lesson 2
1. Lesson 2
1.7. Explore 3
Module 1: Sequences and Series
Arithmetic Sequences Described by Linear Functions
As you can see, arithmetic sequences can be described by linear functions.
Watch Direct and Partial Variation: Arithmetic Sequences to further visualize the connection between arithmetic sequences and linear functions. You will see how the general term of an arithmetic sequence is related to the equation of a line.
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From your work in this lesson, you should have discovered that an arithmetic sequence can be defined as a linear function whose domain consists of natural numbers. 
You may have noticed that the equation of a linear function corresponds to the general-term expression of an arithmetic sequence. Use Arithmetic Sequences Versus Linear Functions to confirm your understanding of the relationship between an arithmetic sequence and a linear function.
Go to pages 14 to 15 of the textbook and work through “Example 4,” which demonstrates the relationship between an arithmetic sequence and a linear function. Read the problem and focus on the wording. Then read the solutions with particular focus on “Method 2: Use a Graph.” As you read, look for answers to the following questions:
- What is the significance of the phrase “plus $42/hr or portion of an hour”?
- When is it appropriate to model a problem using an arithmetic sequence?
- What property of the graph corresponds to the common difference of the arithmetic sequence?
Self-Check 1
Check your understanding of arithmetic sequences by completing Arithmetic Sequences Quiz.