# Lesson 4Scott’s WorkoutSolidify 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 push-ups.

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?

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:

## 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.

## Retrieval

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

### 2.

#### 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 away?

### 5.

Which of the variables is represented by ?

Time or distance?

Time

#### B.

Distance

Find the slope for each representation given.

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