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Ch 17: MTEL Math: Number Patterns & Sequences

About This Chapter

Explore the engaging videos in this chapter to enhance your preparations for the MTEL Mathematics assessment. Refresh your knowledge of number patterns and sequences by exploring arithmetic sequences, geometric sequences, the binomial theorem and more.

MTEL Math: Number Patterns & Sequences - Chapter Summary

You can use this in-depth look at number patterns and sequences to improve your ability to succeed on the MTEL Mathematics assessment. After reviewing the lessons in this chapter, you will be able to:

  • Define the mathematical sequence, and describe finite and infinite sequences
  • Explain how to find the common difference in arithmetic sequences
  • Find and classify an arithmetic sequence, and explain how and why to use the general term of an arithmetic sequence
  • Evaluate and write variable expressions for arithmetic sequences, and work with geometric sequences
  • Share how and why to use the general term of a geometric sequence, and find and classify geometric sequences
  • Describe the Fibonacci sequence, Pascal's triangle, the binomial theorem and factorial notation
  • Detail how to use recursive rules for arithmetic, algebraic and geometric sequences

The subject matter experts in this chapter present the lessons in an entertaining fashion, making your studying process fun. The lessons are highly effective and efficient, averaging just 10 minutes each while providing you with the definitions and examples of number patterns and sequences you need to succeed on the test.

MTEL Math: Number Patterns & Sequences Chapter Objectives

This MTEL Mathematics: Number Patterns & Sequences chapter helps you study for exam topics found in the patterns, relations and algebra subarea of the assessment. This subarea constitutes about 23% of the total test and consists multiple-choice questions. Use the lessons in this chapter to get closer to your goal of earning the minimum passing score of 240 on the exam and securing the licensure required to teach math in Massachusetts classrooms.

This subject-matter test consists of 100 multiple-choice questions and two open-response assignments. It is taken on a computer and lasts four hours with an additional 15 minutes dedicated to a nondisclosure agreement and computer-based test (CBT) tutorial. You can make sure you're comfortable answering questions on the test by taking self-assessment quizzes in this chapter that feature questions similar in format and content. A chapter exam is also available to enhance your preparations for the assessment.

15 Lessons in Chapter 17: MTEL Math: Number Patterns & Sequences
Test your knowledge with a 30-question chapter practice test
What is a Mathematical 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!

Introduction to Sequences: Finite and Infinite

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.

Arithmetic Sequences: Definition & Finding the Common Difference

3. 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 to Find and Classify an Arithmetic Sequence

4. 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!

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.

How to Evaluate & Write Variable Expressions for Arithmetic Sequences

6. How to Evaluate & Write Variable Expressions for Arithmetic Sequences

Being able to figure out sequences as well as describe them are some of the most important skills in math. In this lesson, we learn how to evaluate and write arithmetic sequences and geometric sequences.

Working with Geometric Sequences

7. 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!

Finding and Classifying Geometric Sequences

8. 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!

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.

Fibonacci Sequence: Examples, Golden Ratio & Nature

10. Fibonacci Sequence: Examples, Golden Ratio & Nature

The Fibonacci sequence is seen all around us. Learn how the Fibonacci sequence relates to the golden ratio and explore how your body and various items, like seashells and flowers, demonstrate the sequence in the real world.

Pascal's Triangle: Patterns & History

11. Pascal's Triangle: Patterns & History

In this lesson, you will learn about some of the many patterns found within Pascal's triangle, a set of numbers that has been loved by mathematicians for centuries.

What is the Binomial Theorem?

12. What is the Binomial Theorem?

While the F.O.I.L. method can be used to multiply any number of binomials together, doing more than three can quickly become a huge headache. Luckily, we've got the Binomial Theorem and Pascal's Triangle for that! Learn all about it in this lesson.

How to Use Factorial Notation: Process and Examples

13. 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.

Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

14. 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.

Special Sequences and How They Are Generated

15. 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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Other Chapters

Other chapters within the MTEL Mathematics (09): Practice & Study Guide course

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