4-7 Sequences and Functions
Objectives
To identify and extend patterns in sequences
To represent arithmetic sequences using function notation
Lesson Vocabulary
- sequence
- term of a sequence
- arithmetic sequence
- common difference
In the Solve It, the numbers of pieces of wood used for 1 section of fence, 2 sections of fence, and so on, form a pattern, or a sequence. A sequence is an ordered list of numbers that often form a pattern. Each number in the list is called a term of a sequence.
Essential Understanding When you can identify a pattern in a sequence, you can use it to extend the sequence. You can also model some sequences with a function rule that you can use to find any term of the sequence.
Problem 1 Extending Sequences
Describe a pattern in each sequence. What are the next two terms of each sequence?
Plan
How can you identify a pattern?
Look at how each term of the sequence is related to the previous term. Your goal is to identify a single rule that you can apply to every term to produce the next term.
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A pattern is “add 3 to the previous term.” So the next two terms are
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A pattern is “multiply the previous term by 2.” So the next two terms are
Table of Contents
- 2-1 and 2-2 Solving One- and Two-Step Equations
- 2-3 Solving Multi-Step Equations
- 2-4 Solving Equations With Variables on Both Sides
- 2-5 Literal Equations and Formulas
- 2-6 Ratios, Rates, and Conversions
- 2-7 and 2-8 Solving Proportions and Using Similar Figures
- 2-9 Percents
- 2-10 Change Expressed as a Percent
- 3-1 Inequalities and Their Graphs
- 3-2 Solving Inequalities Using Addition or Subtraction
- 3-3 Solving Inequalities Using Multiplication or Division
- 3-4 Solving Multi-Step Inequalities
- 3-5 Working With Sets
- 3-6 Compound Inequalities
- 3-7 Absolute Value Equations and Inequalities
- 3-8 Unions and Intersections of Sets
- Chapter 1 Foundations for Algebra
- Chapter 2 Solving Equations
- Chapter 3 Solving Inequalities
- Chapter 4 An Introduction to Functions
- Chapter 5 Linear Functions
- Chapter 6 Systems of Equations and Inequalities
- Chapter 7 Exponents and Exponential Functions
- Chapter 8 Polynomials and Factoring
- Chapter 9 Quadratic Functions and Equations
- Chapter 10 Radical Expressions and Equations
- Chapter 11 Rational Expressions and Functions
- Chapter 12 Data Analysis and Probability