# Modeling from a Sequence

### New York State Common Core Math Algebra I, Module 5, Lesson 5

Worksheets for Algebra I, Module 5, Lesson 5 (pdf)

Student Outcomes

• Students recognize when a table of values represents an arithmetic or geometric sequence. Patterns are present in tables of values. They choose and define the parameter values for a function that represents a sequence.

Modeling from a Sequence

Classwork

Opening Exercise

A soccer coach is getting her students ready for the season by introducing them to High Intensity Interval Training (HIIT). She presents the table below with a list of exercises for a HIIT training circuit and the length of time that must be spent on each exercise before the athlete gets a short time to rest. The rest times increase as students complete more exercises in the circuit. Study the chart and answer the questions below. How long would the tenth exercise be? If a player had 30 minutes of actual gym time during a period, how many exercises could she get done? Explain your answers.

Example 1

Determine whether the sequence below is arithmetic or geometric, and find the function that will produce any given term in the sequence:
16, 24, 36, 54, 81, …
Is this sequence arithmetic?
Is the sequence geometric?
What is the analytical representation of the sequence?

Exercises

Look at the sequence and determine the analytical representation of the sequence. Show your work and reasoning.

1. A decorating consultant charges \$50 for the first hour and \$2 for each additional whole hour. How much would 1,000 hours of consultation cost?
2. The sequence below represents the area of a square whose side length is the diagonal of a square with integer side length 𝑛. What would be the area for the 100th square? Hint: You can use the square below to find the function model, but you can also just use the terms of the sequence.
3. What would be the tenth term in the sequence?

Lesson Summary

A sequence is a list of numbers or objects in a special order.

• An arithmetic sequence goes from one term to the next by adding (or subtracting) the same value.
• A geometric sequence goes from one term to the next by multiplying (or dividing) by the same value.
• Looking at the difference of differences can be a quick way to determine if a sequence can be represented as a quadratic expression.

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