The purpose of this lesson is for students to understand what makes a sequence an arithmetic sequence and to connect it to the idea of a linear function. Arithmetic sequences are characterized by adding a constant value to get from one term to the following term, just as linear functions are characterized by a constant rate of change.

Building from their thinking about geometric sequences, students begin this lesson comparing three different sequences. By articulating how the sequences are alike and different, they demonstrate the need for precise language (MP6). Next, students consider two arguments for what type of sequence is represented in a table, and then use a graph of the sequence to justify why it could be arithmetic. Throughout the lesson, students will work with and create different representations of functions.

Math Community
In this lesson, students review the themes that arose when they shared their initial thoughts in Exercise 1 about what they think it should look like and sound like to do math together as a community. Students then have a chance to both affirm and add to the ideas that were generated.