# Ch 6: Number Patterns

### About This Chapter

## Number Patterns - Chapter Summary

Let instructors in this number patterns chapter introduce you to some of the practical applications of tables, graphs, sequences and series. Begin your studies by comparing explicit expressions with recursive processes and examine the uses of deductive and inductive reasoning in geometry.

You can also explore the differences between infinite and finite sequences, as well as sequences resulting from the repeated addition or multiplication of terms. Instructors walk you through the formulas used to find any term in these arithmetic and geometric sequences. They also cover the steps required to solve for the total number in an arithmetic or geometric series.

If you'd like to delve further into recursive sequences, there are lessons discussing why the Fibonacci sequence is often used to describe the golden ratio appearing in nature. You can also learn how to use the concepts covered in this chapter to solve finance problems involving compound and continuing interest and annuities. This chapter addresses the following main topics:

- Mathematical induction
- Explicit expressions
- Recursive processes
- Arithmetic and geometric series
- Interest problems

Our video lessons are taught by experienced instructors who provide numerous examples, illustrations and sample problems to help you understand number patterns and their practical applications. To help reinforce your comprehension of the materials, there are lesson transcripts for quick reference and quizzes you can use to assess your grasp of the material.

### 1. Using Tables and Graphs in the Real World

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

### 2. Using Iterative Processes to Solve Math Problems

In this lesson, we will discuss what an iterative process is in general, and then we will look at how to use various iterative processes to solve problems in mathematics and the real world.

### 3. 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.

### 4. 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!

### 5. 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!

### 6. 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.

### 7. 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!

### 8. 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.

### 9. 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.

### 10. How to Solve Interest Problems: Steps & Examples

If you want to know how your money can earn money, then it's essential to learn about solving interest problems. In this lesson, we'll practice calculating interest amounts and interest rates.

### 11. Compounding Interest Formulas: Calculations & Examples

Compound interest is a great way to have your money work for you. In this lesson, find out the formula for calculating compound interest and practice using the formula with several examples.

### 12. What is Annuity? - Definition & Formula

In this lesson, you'll learn about payments that occur at regular time intervals, or in financial terms, annuities. Afterwards, test your understanding of the lesson with a quiz.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards