About This Chapter
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
|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.|
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. 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.
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.
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Other chapters within the Algebra II Textbook course
- Algebra II: Basic Arithmetic Review
- Algebra II: Algebraic Expressions and Equations Review
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Matrices and Determinants
- Algebra II: Absolute Value Review
- Algebra II: Polynomials
- Algebra II: Factoring
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Quadratic Equations
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Conic Sections
- Algebra II: Sets
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry