About This Chapter
Algebra: Sequences and Series
Many terms used in mathematics are terms that are used in everyday life, such as sequence and series. The definition of sequence - a list of objects in a specific order - is the same in any application. For example, a sequence of events is a list of events that are in a particular order. A sequence of numbers is a list of numbers in a particular order. A series, in situations other than math, is the same thing as a sequence. You will soon learn through the lessons how to distinguish between the two terms in a mathematical context.
The video lessons will jump right into the concept of sequences. You'll learn the different types of sequences that you may deal with in a mathematical situation (arithmetic, geometric, etc.). Finding and classifying sequences will also be discussed. To help ensure you understand, you'll be given examples of how sequences show up in real life, too.
The lessons will move into explaining how a series differs from a sequence. A discussion of summation notation will also be included. You'll learn about calculating arithmetic series and even get to try your hand at some practice problems. Geometric series will also be discussed and practice problems presented.
Through these video lessons, the concepts of sequences and series will be laid out in a simple and direct manner. You'll be taught in a way that allows you to learn how to apply these concepts in your day-to-day activities, which helps make them easier to understand and the concepts seem more concrete.
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!
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Other chapters within the Math 101: College Algebra course
- Foundations of Linear Equations
- Matrices and Absolute Value
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Rational Expressions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Studying for Math 101