1. Lesson 5

1.6. Explore 2

Mathematics 20-1 Module 1

Module 1: Sequences and Series

 

Determining the Sum of a Geometric Series

 

In Lesson 3 you derived the formulas for evaluating an arithmetic series by applying Gauss’ method. The method was first applied to a specific series, and then the method was applied to the general case.

 

This is a play button that opens Sum of a Series Pop!

Watch Sum of a Series Pop! to see one strategy for determining the sum of a geometric series. As you watch, pay attention to the pop-up bubbles that appear. You may want to pause the video at these points in order to think about the questions in the pop-ups.

You have now been exposed to two possible ways to find the sum of a series:

  • the way used in the chessboard activity from Try This 1

  • the way used in Sum of a Series Pop!
Try This 2

 

In Try This 2 you will construct a formula to describe the sum of any geometric series. You will use the method from Sum of a Series Pop! However, instead of beginning with a specific geometric series, you will begin with a general geometric series made up of variables.

 

Begin with a general geometric series written in full:

 

 

Sn = a + ar + ar2 + ar3 + + arn−1

 

This is a play button that opens Geometric Series Proof Sorter.

Use this general series and Geometric Series Proof Sorter to construct a formula to describe the sum of any geometric series.