Learning Resources

Outcomes

In this lesson you will

• Solve problems by identifying and extending number sequences.
• Use geometric and number patterns to create arithmetic sequences.
• Explore the properties of arithmetic sequences and discover that the differences between successive terms form another sequence of constant numbers called the common difference.
• Use the constant difference and the value of the first term to develop a rule to describe any term of the arithmetic sequence.
• Develop the expression  t_n = t₁ + (n - 1)d for an arithmetic sequence.
• Explore graphs of arithmetic sequences.

By the end of this section you should be able to:

• Demonstrate an understanding of patterns that are arithmetic, power, and geometric, and relate them to corresponding functions.
• Analyze tables and graphs to distinguish between linear, quadratic, and exponential relationships.
• Sketch graphs from descriptions, tables, and collected data.

Introduction

In this section you will examine properties of number sequences. You will solve problems involving sequences by identifying and extending patterns. You will classify arithmetic and power sequences by forming a sequence of differences between successive terms in a sequence or table.

You will use the first-level common difference to create a linear function used to generate a given arithmetic sequence. You will also examine and find quadratic functions that generate sequences.

This section should take you about 4 hours to complete.

Prerequisites

• The definitions and distinguishing characteristics of linear functions.
• How to use symbols to represent linear functions.
• How to calculate the slope of a line.