# Ch 27: Mathematical Sequences and Series: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other precalculus work.
- Identify the math sequences and series concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our high school precalculus tutoring solution will benefit any student who is trying to learn math sequences and series and earn better grades. This resource can help students including those who:

- Struggle with understanding factorial notation, summation notation and mathematical series, arithmetic and geometric series or any other math sequences and series topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their mathematical sequences and series unit
- Cope with ADD or ADHD
- Want to get ahead in precalculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning math sequences and series simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live precalculus tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn mathematical sequences and series on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Define piecewise functions.
- Find the domain of piecewise functions.
- Graph piecewise functions.
- Translate piecewise functions.

## Learning Objectives

- Define mathematical sequences.
- Provide examples of finite and infinite sequences.
- Learn how to use factorial notation.
- Explain how to use summation notation.
- Discuss the use of arithmetic series in algebra.
- Calculate an arithmetic series.
- Determine the common difference for arithmetic sequence.
- Describe how to use the general term of an arithmetic sequence.
- Find the sum of the first n terms of an arithmetic sequence.
- Classify arithmetic and geometric sequences.
- Explain how to use the general term of a geometric sequence.
- Find the sum of the first n terms of a geometric sequence.
- Become familiar with the formula for infinite geometric series.
- Calculate a geometric series.
- Use recursion formulas for arithmetic, algebraic and geometric sequences.
- Use sigma notation to represent the sum of a series.
- Explain when and how to use mathematical induction.
- Determine the value of an annuity.
- Expand a binomial using the binomial theorem.
- Explain how special sequences are generated.

### 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!

### 12. 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!

### 13. Finding and Classifying Geometric Sequences

Want your YouTube video to get a lot of hits? Besides including a cute baby or an adorable cat, getting your video to have a big common ratio is the key. Learn what I'm talking about here!

### 14. 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.

### 15. 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.

### 16. 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.

### 17. How to Calculate a Geometric Series

If you're not satisfied with knowing how many views your YouTube video will get any one day and need to know how many total views you're getting, geometric series are for you! Learn more in this lesson.

### 18. 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.

### 19. Arithmetic and Geometric Series: Practice Problems

There are many different types of problems concerning series and sequences - including some that are pretty abstract. From bouncing balls to adding up odd numbers, test your skills here with additional arithmetic and geometric series practice!

### 20. 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.

### 21. 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.

### 22. 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.

### 23. 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.

### 24. 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.

### 25. Finite Sequence: Definition & Examples

After completing this lesson, you will be able to identify a finite sequence and different types of finite sequences. You will also be able to distinguish mathematical patterns of finite sequences.

### 26. Geometric Series: Formula& Example

A geometric series is a series of numbers with a constant ratio between successive terms. Keep reading to discover more about geometric series, learn how to find the common ratio, and take a quiz to measure your understanding.

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### Other Chapters

Other chapters within the High School Precalculus: Tutoring Solution course

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