Ch 21: Algebra II: Sequences and Series

About This Chapter

Watch online video lessons to learn about sequences and series in algebra, including the formulas for various types. Each lesson is accompanied by a short multiple-choice quiz you can use to check your understanding of these math topics.

Algebra II: Sequences and Series - Chapter Summary and Learning Objectives

In this chapter, you'll become familiar with the concept of sequences, which are sets for numbers in a particular order. A sequence can be finite, which means it has an end, or infinite, which means it goes on forever. A series is related to a sequence and is the sum of numbers in an infinite sequence. By the end of this chapter, you should be able to:

  • Define infinite and finite sequences and give examples
  • Use factorial and summation notation
  • Define and write terms of an arithmetic sequence
  • Explain the formula for the sum of an infinite geometric series
  • Show the sum of a series using sigma notation
  • Explain how to generate special sequences and name some examples

Video Objective
Introduction to Sequences: Finite and Infinite In this lesson, we'll examine what finite and infinite sequences are and learn to determine the sequence's particular terms.
How to Use Factorial Notation: Process and Examples You'll get information on using factorial notation, including when it's appropriate. Examples will help you become comfortable with the process.
How to Use Series and Summation Notation: Process and Examples Next, we'll look at using series and summation notation.
Arithmetic Sequences: Definition and Finding the Common Difference In this lesson, we'll learn what an arithmetic sequence is and how to find the common difference. We'll also learn to write terms for the sequence.
How and Why to Use the General Term of an Arithmetic Sequence Here, we examine the formula for an arithmetic sequence's general term and discuss when to use it.
The Sum of the First n Terms of an Arithmetic Sequence You'll learn how and when to utilize the formula that gives us the sum of an arithmetic sequence's first n terms.
Understanding Arithmetic Series in Algebra Now, we'll examine examples that help us understand what an arithmetic series is. We'll also learn to determine an arithmetic sequence's common difference.
Working with Geometric Sequences In this lesson, we'll study geometric sequences and learn what they are, how to determine the common ratio and write terms.
How and Why to Use the General Term of a Geometric Sequence You'll get information on using this formula and when it should be applied.
The Sum of the First n Terms of a Geometric Sequence You'll learn how and when to utilize the formula that gives us the sum of a geometric sequence's first n terms.
Understand the Formula for Infinite Geometric Series Now, we'll decide how and when to use the formula that gives us the sum of an infinite geometric series.
Using Recursive Rules for Arithmetic, Algebraic and Geometric Sequences Here, recursion formulas are examined.
Using Sigma Notation for the Sum of a Series You'll learn how to use sigma notation to depict the sum of a series.
Mathematical Induction: Uses and Proofs This lesson gives the definition and uses of mathematical induction and shows you, with examples, how to use it to prove statements.
How to Find the Value of an Annuity You'll put these rules to practical use by utilizing them to determine an annuity's value.
How to Use the Binomial Theorem to Expand a Binomial This lesson depicts how to expand a binomial with the binomial theorem.
Special Sequences and How They are Generated Learn about special sequences including Fibonacci numbers and triangular numbers and get information about their properties.

17 Lessons in Chapter 21: Algebra II: Sequences and Series
Test your knowledge with a 30-question chapter practice test
Introduction to Sequences: Finite and Infinite

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.

How to Use Factorial Notation: Process and Examples

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.

How to Use Series and Summation Notation: Process and Examples

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.

Arithmetic Sequences: Definition & Finding the Common Difference

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.

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

The Sum of the First n Terms of an Arithmetic Sequence

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.

Understanding Arithmetic Series in Algebra

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.

Working with Geometric Sequences

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!

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

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.

The Sum of the First n Terms of a Geometric Sequence

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.

Understand the Formula for Infinite Geometric Series

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.

Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

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.

Using Sigma Notation for the Sum of a Series

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.

Mathematical Induction: Uses & Proofs

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.

How to Find the Value of an Annuity

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.

How to Use the Binomial Theorem to Expand a Binomial

16. How to Use the Binomial Theorem to Expand a Binomial

In this video lesson, you will see what the binomial theorem has in common with Pascal's triangle. Learn how you can use Pascal's triangle to help you to easily expand a binomial.

Special Sequences and How They Are Generated

17. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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