Learning Resources

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Outcomes

In this lesson you will learn

• how to write a recursive formula for a geometric sequence
• how to write a non-recursive (explicit) formula for a geometric sequence
• how to generate terms in a geometric sequence

By the end of this section students will be able to:

• demonstrate an understanding of recursive formulas
• model problem situations using discrete structures such as sequences and recursive formulas
• represent arithmetic and geometric sequences as ordered pairs and discrete graphs
• represent series in expanded form and using sigma notation
• develop, analyze and apply algorithms to generate terms in a sequence
• develop, analyze and apply algorithms to determine the sum of a series
• demonstrate understanding for recursive formulas, and how recursive formulas relate to a variety of sequences

Introduction

This section focuses on geometric and other types of recursive sequences. Once again, you will be graphing sequences and developing formulas, but this time to find the n^th term of a geometric sequence and for adding the terms of a geometric series.

By the end of this section, you will have done sufficient work on recursive formulas that you will be quickly able to note the advantages and disadvantages of using them to describe sequences. 

It should take about 4 hours to complete this section.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• the definition of a geometric sequence and readily give examples of such
• what is meant by the phrase "common ratio" as it relates to geometric sequences
• how to work with percentages
• exponential notation
• how to use logarithms to solve an exponential equation in which like bases cannot be found