# Lesson 4 Scott’s Workout Solidify Understanding

## Learning Focus

Model a sequence using a table, graph, and explicit and recursive equations.

How do I see the change between figures in each representation?

How can I tell if a sequence is arithmetic, geometric, or neither?

How are explicit equations different than recursive equations?

What are the advantages of using an explicit equation versus a recursive equation?

## Open Up the Math: Launch, Explore, Discuss

Scott has decided to add push-ups to his daily exercise routine. He is keeping track of the number of push-ups he completes each day in the given bar graph, with day 1 showing he completed

After four days, Scott is certain he can continue this pattern of increasing the number of push-ups he completes each day.

### 1.

How many push-ups will Scott do on day

### 2.

Model the number of push-ups Scott will complete on any given day. Include a table, a graph, and both recursive and explicit equations.

Table:

Recursive equation:

Explicit equation:

### 3.

What type of sequence is your model for the number of push-ups that Scott did? How do you know?

## Ready for More?

Aly is also including push-ups in her workout and says she does more push-ups than Scott because she does fifteen push-ups every day. Is she correct? Explain.

## Takeaways

Finding the common difference in each representation of an arithmetic sequence:

Table:

Explicit equation:

Recursive equation:

Graph:

## Adding Notation, Vocabulary, and Conventions

Recursive notation:

## Vocabulary

- independent variable / dependent variable
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we modeled a real-world situation with a table, graph, and equations, both explicit and recursive. We learned the mathematical notation for writing recursive equations and how to identify the common difference in each of the representations.

Use the explicit function equations below to find the indicated values.

### 1.

#### a.

#### b.

### 2.

#### a.

#### b.

For problems 3–5, use the graph to answer the questions. The graph is a sketch that was created to represent the distance traveled by a biker over time.

### 3.

How far away are they at

### 4.

How long does it take them to reach

### 5.

Which of the variables is represented by

Time or distance?

#### A.

Time

#### B.

Distance

Find the slope for each representation given.