# Ch 25: Solving Problems with Sequences & Series

### About This Chapter

## Solving Problems with Sequences and Series - Chapter Summary

You can quickly prepare for solving problems with sequences and series as you utilize the information in this chapter. These brief, concise lessons will cover necessary elements of this topic. You will review such information as how to find and classify an arithmetic sequence, finding and classifying geometric sequences, and the definition of convergent sequence. Once you have completed the lessons in this chapter you should be able to:

- Define mathematical sequence
- Understand summation notation and mathematical series
- Calculate an arithmetic series
- Work problems using arithmetic and geometric series
- Give examples of convergent sequence

These interesting video lessons will reinforce the knowledge you have about solving problems with sequences and series. This chapter conveniently enables you to study in a variety of settings and at your own pace. You can assess your knowledge after each lesson by taking the quiz to see how well you grasp the concept. This will help as you figure out which skills need a little more attention. Another bonus is having the subject-matter experts available to help you as needed.

### 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. 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!

### 3. 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!

### 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 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.

### 6. 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.

### 7. 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!

### 8. Convergent Sequence: Definition, Formula & Examples

This lesson will explore sequences that are convergent. We will define convergent sequences, and look at how to determine if a given sequence is convergent using formulas and limits.

### 9. Recursive Sequence: Formula & Overview

One of the most famous recursive sequences is the Fibonacci sequence. In this lesson, learn what makes the Fibonacci sequence a recursive sequence, and discover how you can recognize and create your own.

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### Other Chapters

Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course

- Overview of Mathematical Reasoning
- Introduction to Mathematical Problem Solving
- NES Math: Properties of Real Numbers
- Understanding Relations & Functions
- Overview of Linear Functions & Equations
- Quadratic Equations, Functions & Inequalities
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Probability: Principles & Techniques
- Overview of Discrete Mathematics
- Performing Operations on Matrices & Vectors
- NES Mathematics Middle Grades & Early Secondary Flashcards