1. Lesson 5

1.13. Lesson 5 Summary

Mathematics 20-1 Module 1

Module 1: Sequences and Series

 

Lesson 5 Summary
 

This is an illustration of an ascending escalator and a descending escalator. Items that appreciate in value are shown on the ascending escalator. Items that depreciate in value are shown on the descending escalator.

 

In this lesson you investigated the following questions:

  • In what ways can mathematical formulas be derived?

  • How are geometric series used in finance?

Geometric series represent the sum of the terms of a geometric sequence. It is not always convenient to add the individual terms of a geometric series due to the large number of terms. In this lesson you derived two formulas that can be used to determine the sum of any number of terms in a geometric series.

 

You practised two commonly accepted approaches for formula derivation. The first approach is to start with a specific case using actual numerical values. The general case, or formula, is then deduced by substituting variables for the numerical values. This is the method you used to derive the first geometric series formula,

 

The second approach involves combining known formulas or relationships to create a new formula. This is the method you used to derive the second geometric series formula. For the second formula, you combined the general term of a geometric sequence with the first geometric series formula. This created

 

You also investigated problems that can be solved with geometric series, such as the problem of the bouncing ball and the investment questions in Project Connection.

 

In the final lesson of this module you will consider how you can add the terms of an infinite geometric series.