# Ch 16: Notation, Sequences & Series

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### About This Chapter

## Notation, Sequences & Series - Chapter Summary

The lessons in this chapter examine various types of sequences and how they are used. You'll see examples of factorial notation and learn to use sigma notation. Other lessons explore series and summation notation.

Our instructors explain and give examples of how to calculate the value of an annuity as well as the uses for mathematical induction. They discuss recursive rules for several types of sequences, too. After watching all these lessons, you should know how to:

- Define finite and infinite sequences
- Find the common difference in arithmetic sequences
- Determine when to use the general term of an arithmetic sequence
- Explain arithmetic series in algebra
- Work with geometric sequences
- Use the formula for infinite geometric series
- Show proofs of mathematical induction
- Explain how special sequences are generated

The lessons in this chapter are taught by expert instructors who break down the topic in a way that's easy to understand. Each lesson also includes a multiple-choice quiz so you can assess your knowledge and see where you need further study. You can easily find certain topics in the lessons with the timeline's jump feature. Written transcripts that accompany the lessons highlight key terms and concepts you'll need to know about.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. Working with Geometric Sequences

In this video lesson, we'll learn how to recognize when a sequence of numbers is a geometric sequence, how to find the common ratio and how to expand a sequence to as many numbers as we want!

### 9. How and Why to Use the General Term of a Geometric Sequence

Watch this video lesson to learn the formula for the general term of a geometric sequence. You will learn how to write your own general term given a particular geometric sequence as well as the reason for doing this.

### 10. The Sum of the First n Terms of a Geometric Sequence

Watch this video lesson to learn how you can find the total of a geometric sequence up to a certain point. Learn the formula that you can use to help you find your answer.

### 11. Understand the Formula for Infinite Geometric Series

Watch this video lesson to learn how to calculate the sum of an infinite geometric series. Learn about the interesting thing that happens when your common ratio is less than one.

### 12. Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

When dealing with sequences in math, both algebraic and geometric, we come across recursive rules. Watch this video lesson to learn how recursion works and how you can use a recursive rule to get to your next number using a previous number.

### 13. Using Sigma Notation for the Sum of a Series

In math, we have a notation for a lot of things. When you need to sum up a series, we also have a notation for that. You will learn about this notation, called Sigma notation, in this video lesson.

### 14. Mathematical Induction: Uses & Proofs

Watch this video lesson to learn about mathematical induction and how you can use it to prove mathematical statements. See how it is similar to falling dominoes.

### 15. How to Find the Value of an Annuity

Want to see how much money you will have in the future if you make a set payment every month towards your annuity? Then watch this video lesson for the formula and how to use it.

### 16. Special Sequences and How They Are Generated

Sequences are interesting things in math and in nature. The most interesting thing is that these sequences have a pattern to how they are generated. We will learn about a few of them in this video lesson.

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### Other Chapters

Other chapters within the Accuplacer College Level Math Test: Practice & Study Guide course

- Operations with Basic Algebraic Expressions
- Arithmetic with Rational Expressions
- Factoring in Algebra
- Expanding Polynomials
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Solving Systems of Linear Equations
- Geometric Angles & Shapes
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Graphs of Algebraic Functions
- Complex and Imaginary Numbers
- Matrices and Determinants in Algebra
- Combinatorics
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Understanding Exponential & Logarithmic Functions
- Trigonometric Functions & Equations