About This Chapter
Below is a sample breakdown of the Mathematical Sequences & Series chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Mathematical sequences and series||Finite sequence, infinite sequence, general term, particular term, factorial notation, and summation notation|
|Tuesday||Arithmetic series||Sequences vs. series, common difference, and arithmetic series formula|
|Wednesday||Arithmetic & geometric sequences||Arithmetic sequence, linear relationship, arithmetic formulas, geometric sequence, common ratio, nth term, nth term general rule, an=a1r^n-1, and the sum formula|
|Thursday||Further studies in series and sequences||Geometric series, geometric series formula, (a_1)((1 - r^n)/(1 - r), infinite series, proving formulas, recursive rule, recursive formula, and formula adjustments|
|Friday||The application of theorems and notations||Sum of a series, Sigma notation, mathematical induction, annuity, determining future values, binomial theorem, expand, Pascal's triangle, expanding a binomial, special sequence, triangular sequence, tetrahedral sequence, square sequence, cube sequence, and the Fibonacci 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!
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.
3. 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.
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 Use Series and Summation Notation: Process and Examples
Have you ever seen a sideways M on a math test and wondered what it meant? In this video lesson, learn about the notation that we use to show that we want to sum something up. Learn how to use it and see some examples of it in use.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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!
12. 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!
13. 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!
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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!
20. Using Sigma Notation for the Sum of a Series
In math, we have a notation for a lot of things. When you need to sum up a series, we also have a notation for that. You will learn about this notation, called Sigma notation, in this video lesson.
21. 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.
22. 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.
23. 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.
24. 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.
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Other chapters within the High School Precalculus Syllabus Resource & Lesson Plans course
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