# Ch 28: Understanding Arithmetic Sequences & Series

### About This Chapter

## Understanding Arithmetic Sequences & Series - Chapter Summary and Learning Objectives

When studying math concepts, it's good to learn from as many resources as possible to get the well-rounded knowledge you need. In this chapter are lessons that focus on understanding arithmetic sequences and series to improve your chances of success on homework, quizzes or a big test. Video lessons provide an in-depth look at definitions, processes and calculations associated with arithmetic sequences and series. Learn more about summation notation, finding the common difference, using the general term of an arithmetic sequence and much more.

Expert instructors with a wealth of math knowledge present the video lessons in a fun and engaging manner. Enjoy learning from the comfort of your home or on the go via your smartphone or tablet. Full transcripts with helpful vocabulary words are available to further enhance your understanding of lesson concepts. If you want to test your knowledge of the lessons, feel free to take self-assessment quizzes and a chapter exam. Taking these steps will help you grasp the following:

- The meaning of a mathematical sequence and finite and infinite sequences
- How to use factorial, series and summation notation
- The arithmetic series in algebra and how it is calculated
- The definition of arithmetic sequences
- Why to use the general term and how to find the common difference of an arithmetic sequence
- The process of finding and classifying an arithmetic sequence

Video | Objective |
---|---|

What is a Mathematical Sequence? | Define the sequence, and identify and describe types of sequences. |

Introduction to Sequences: Finite and Infinite | Describe infinite and finite sequences. |

How to Use Factorial Notation: Process and Examples | Explain why and how factorial notation is used. |

Summation Notation and Mathematical Series | Discuss the meaning of a series, and explain the use of summation notation. |

How to Use Series and Summation Notation: Process and Examples | Learn how and why summation notation is used. |

Understanding Arithmetic Series in Algebra | Review the meaning of arithmetic series, and learn how to determine the common difference in an arithmetic sequence. |

How to Calculate an Arithmetic Series | Understand the process of calculating arithmetic series. |

Arithmetic Sequences: Definition & Finding the Common Difference | Discover the meaning of the arithmetic sequence, and discover how to find the common difference and write terms of an arithmetic sequence. |

How and Why to Use the General Term of an Arithmetic Sequence | Examine why and how to use the formula for an arithmetic sequence's general term. |

The Sum of the First n Terms of an Arithmetic Sequence | Find out why and how to use an arithmetic sequence's formula for the sum of the first n terms. |

How to Find and Classify an Arithmetic Sequence | Study the process of finding and classifying an arithmetic sequence. |

### 1. What is a Mathematical Sequence?

Math is often the most fun when it acts like a puzzle to be solved. The branch of math where this is the most true involves sequences. Get an introduction to the basics and important vocabulary, as well as learn where sequences appear in nature!

### 2. Introduction to Sequences: Finite and Infinite

In this video lesson, we will learn about the many patterns that are possible in sequences. See how some sequences stop after a while and how some sequences never stop.

### 3. How to Use Factorial Notation: Process and Examples

Watch this video lesson to learn about factorial notation. Understand what it means so that you can handle it like a pro. Also see what happens when we divide factorials.

### 4. Summation Notation and Mathematical Series

The capital Greek letter sigma might be most recognizable as a common symbol in a fraternity or sorority, but it's used for some pretty cool math tricks too. In this lesson, learn how to use sigma for things like determining how many seats are in Michigan Stadium.

### 5. How to Use Series and Summation Notation: Process and Examples

Have you ever seen a sideways M on a math test and wondered what it meant? In this video lesson, learn about the notation that we use to show that we want to sum something up. Learn how to use it and see some examples of it in use.

### 6. Understanding Arithmetic Series in Algebra

In this video lesson, we will learn about arithmetic series and how they work. Learn also how to find the pattern of an arithmetic sequence along with finding the sum.

### 7. How to Calculate an Arithmetic Series

In this lesson, you'll learn how to sum up any arithmetic sequence without having to add up each and every term. You'll never guess the circumstances that led to the discovery of this marvelous formula.

### 8. Arithmetic Sequences: Definition & Finding the Common Difference

Watch this video lesson to learn the pattern that defines an arithmetic sequence. Learn how to identify arithmetic sequences as well as find the pattern easily. You will also learn the formula you can use to write any number in your sequence.

### 9. How and Why to Use the General Term of an Arithmetic Sequence

Watch this video lesson to learn the formula for the general term of an arithmetic sequence. Also learn why this formula makes working with an arithmetic sequence much easier.

### 10. The Sum of the First n Terms of an Arithmetic Sequence

In this video lesson, you will learn an easy to use formula for summing an arithmetic sequence. Watch as we use the formula in action and then get a chance to use it yourself as you follow along.

### 11. How to Find and Classify an Arithmetic Sequence

Arithmetic sequences are everywhere, and with a few tricks you learn here, you could end up looking like a psychic the next time you go to a movie or a football game!

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Continuity
- Limits in Precalculus