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Ch 47: NES Math: Sequences & Series

About This Chapter

Let us help you review information on sequences and series in mathematics, including the Fibonacci Sequence. These video lessons and other tools for study can aid in your preparation for the NES Math test.

NES Math: Sequences & Series - Chapter Summary

Use the lessons in this chapter of our study guide to refresh your knowledge of arithmetic as well as algebraic and geometric sequences as you prepare for the NES Math test. Our lively videos, short quizzes and other study aids can help you brush up on topics such as:

  • Finite and infinite sequences
  • When to use the general term of an arithmetic sequence
  • Arithmetic series in algebra
  • Geometric sequences
  • How the formula for infinite geometric series works
  • Definition of the Golden Ratio and examples from nature
  • Recursive rules for arithmetic, algebraic and geometric sequences

These lessons average about five minutes in length, and they're accessible via tablet, laptop or smartphone. A short quiz follows each lesson, and there is a comprehensive exam at the end of each chapter. These tests provide a good way to assess your learning. The answer keys include links back to the lessons, so if you answer a question incorrectly, it's easy to just pop back to that passage for more review.

NES Math: Sequences & Series Chapter Objectives

Arizona, New Mexico, Oregon, Washington and Wisconsin require passing the NES Math test as one of the conditions for obtaining certification to teach mathematics at the secondary level. The test is administered on computer and consists entirely of multiple-choice questions, asking you to choose the correct answer to a question or math problem from several options. The questions in our chapter exam and the lesson quizzes are in this format, offering a chance to become familiar with this type of test.

The NES Math test's questions are divided into five content domains. Questions on the material in the Sequences & Series chapter are in the Statistics, Probability and Discrete Mathematics content domain. This content domain makes up 19% of the test's total scoring.

11 Lessons in Chapter 47: NES Math: Sequences & Series
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.

Arithmetic Sequences: Definition & Finding the Common Difference

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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.

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.

Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

11. 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.

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Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course

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