# Lesson 3

Different Types of Sequences

### Lesson Narrative

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.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and in writing) arithmetic and geometric sequences.
• Determine the rate of change of an arithmetic sequence.
• Interpret tables and graphs to determine if a sequence is arithmetic or geometric.

### Student Facing

• Let’s look at other types of sequences.

### Student Facing

• I can explain what it means for a sequence to be arithmetic or geometric.

Building On

Building Towards

### Glossary Entries

• arithmetic sequence

A sequence in which each term is the previous term plus a constant.