About This Chapter
Working with Sequences & Series - Chapter Summary and Learning Objectives
Develop your understanding of how to work with sequences and series with this chapter. These lessons will help you assess the theorems and principles associated with sequences and series to ensure your understanding. As you complete these lessons, you'll be increasing what you know about:
- Recursive rules
- Types of series and special sequences
- Mathematical induction and the value of an annuity
- The binomial theorem and the fundamental counting principle
- Math combinations and permutations
|Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences||Analyze the uses of recursive formulas.|
|Arithmetic and Geometric Series: Practice Problems||Evaluate real life examples of arithmetic and geometric series|
|Mathematical Induction: Uses & Proofs||Focus on explaining and learning to use mathematical induction.|
|How to Find the Value of an Annuity||Consider the steps to finding the value of an annuity.|
|How to Use the Binomial Theorem to Expand a Binomial||Assess the uses of the binomial theorem.|
|Special Sequences and How They Are Generated||Classify special sequences by name.|
|How to Use the Fundamental Counting Principle||Appraise the uses of the fundamental counting principle.|
|Math Combinations: Formula and Example Problems||Categorize and understand various combinations.|
|How to Calculate a Permutation||Break down the steps for calculating a permutation.|
1. 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.
2. 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!
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. 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.
5. 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.
6. 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.
7. How to Use the Fundamental Counting Principle
There are many situations in which you will have to make several decisions simultaneously. The fundamental counting principle will help you determine how many different possible outcomes there are when you have to make multiple simultaneous decisions.
8. Math Combinations: Formula and Example Problems
Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.
9. How to Calculate a Permutation
A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.
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Other chapters within the Honors Precalculus Textbook course
- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Sets & Probability
- Limits in Precalculus