1. Lesson 4

Mathematics 20-1 Module 1

Module 1: Sequences and Series

 

Lesson 4: Geometric Sequences

 

Focus

 

This shows a photo of a young woman with her hands raised while sitting in the driver’s seat of an orange car. She holds the keys to the car in her right hand.

© brankatekic/21709824/Fotolia

Do you have your driver’s license? For many people, passing their road test is a huge milestone and another step towards freedom and independence. For many parents, another driver in the family means they can share the responsibility of driving with their children. A new car, however, isn’t cheap. On top of that, there are insurance, fuel, and maintenance costs to owning a vehicle. Nevertheless, buying a car can be a thrilling experience, especially when it’s your first car!

 

Many people borrow money to buy a vehicle. This is called financing the vehicle. The benefit of financing is that you get to use the vehicle right away. The drawback is that you have to pay the interest on the outstanding balance after each month.

 

To keep things predictable for the borrower, lenders use the mathematics of sequences to determine monthly payments.

 

In this lesson you will investigate geometric sequences. Just as you did with arithmetic sequences, you will use discovered patterns to derive rules for determining the general term of a geometric sequence. You will also explore problems, such as those involving compound interest, that can be modelled by geometric sequences.

 

Outcomes

 

At the end of this lesson you will be able to

  • identify assumptions made when identifying a geometric sequence

  • provide and justify an example of a geometric sequence

  • derive a rule for determining the general term of a geometric sequence

  • solve a problem that involves a geometric sequence
Lesson Questions

 

You will investigate the following questions:

  • How are arithmetic sequences and geometric sequences similar and different?

  • How is compound interest an application of geometric sequences?
Assessment


Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 4 Assignment (Download the Lesson 4 Assignment and save it in your course folder now.)

  • course folder submissions from Try This and Share activities

  • additions to Module 1 Glossary Terms and Formula Sheet

  • work under Project Connection
Materials and Equipment

 

You will need a sheet of paper.