Lesson 5

Lesson 5: Geometric Series

 

Focus

 

In an earlier lesson you started to think about your financial goals. These may include major purchases, such as a house or a car. You may have also considered putting money away for college or university, or for an overseas trip.

 

While each of these goals is worthwhile in its own right, the goals are not equal from an investment perspective. The value of the car depreciates over time—in other words, the car’s value goes down as the car ages. A backpacking trip to Europe may provide a lifetime of memories and character-building experiences; however, there is no monetary return on the investment—you cannot make any money from the trip.

 

There are also examples of financial goals that appreciate, or increase, in value over time. One example of this is your post-secondary education. In fact, generally speaking, the more education you have, the higher your earning power after graduating. Another example of an appreciating asset is a house. Homes these days are expensive, but past experience shows that houses increase in value over the long run.

 

This lesson is about geometric series. A geometric series can be used to determine the value of an investment when monthly contributions are made. You will derive and use formulas relating to geometric series. You will study the contexts in which those formulas can be applied, and you will gain an understanding of how geometric series relate to finance.

 

Outcomes

 

At the end of this lesson you will be able to

• derive a rule for determining the sum of n terms of a geometric series
  
  
• determine t1, r, n, or Sn  in a problem that involves a geometric series
  
  
• solve a problem that involves a geometric series

Lesson Questions

 

You will investigate the following questions:

• In what ways can mathematical formulas be derived?
  
  
• How are geometric series used in finance?

Assessment

 

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

• completion of the Lesson 5 Assignment (Download the Lesson 5 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