# Ch 21: Mathematical Sequences and Series

Watch online video lessons to learn about arithmetic series, geometric sequences, factorial notation and more. Complete the quizzes that follow each lesson to test your knowledge of these concepts.

## Mathematical Sequences and Series - Chapter Summary and Learning Objectives

Watch the videos in this chapter to learn how mathematical patterns can be used to solve problems that would be pretty difficult to calculate otherwise. Instructors introduce you to factorial and summation notation, as well as the formulas required to find particular terms in a sequence or determine the sum of a mathematical series. Once you've worked your way through this chapter, you should be able to:

• Find any term in an arithmetic or geometric sequence
• Identify the common difference in an arithmetic sequence
• Recognize the common ratio in a geometric sequence
• Add all terms in an arithmetic sequence
• Find the sum of an infinite geometric series
• Understand how special sequences are generated

Video Objectives
What Is a Mathematical Sequence? Learn how to recognize terms in a sequence. Explore the differences between arithmetic and geometric sequences.
Introduction to Sequences: Finite and Infinite Differentiate between a finite and infinite sequence. Get tips for finding a particular term in a sequence.
How to Use Factorial Notation: Process and Examples Learn what factorial notation is and explain how to use it.
Summation Notation and Mathematical Series Understand how to build a series formula used to solve arithmetic sequences.
How to Use Series and Summation Notation: Process and Examples Get instruction on the proper use of summation notation.
Understanding Arithmetic Series in Algebra Define an arithmetic series. Learn how to find the common difference in an arithmetic sequence.
How to Calculate an Arithmetic Series Discover formulas used to add all the terms in an arithmetic series.
Arithmetic Sequences: Definition & Finding the Common Difference Get tips for writing terms in an arithmetic sequence and finding the common difference.
How and Why to Use the General Term of an Arithmetic Sequence Apply the formula used to find the general term of an arithmetic sequence.
The Sum of the First n Terms of an Arithmetic Sequence Learn how to find the sum of the first n terms of an arithmetic sequence.
How to Find and Classify an Arithmetic Sequence Memorize the two formulas used to find any term in an arithmetic sequence.
Working with Geometric Sequences Understand how to write terms of a geometric sequence and find the common ratio.
Finding and Classifying Geometric Sequences Practice creating a formula to find terms of a geometric sequence.
How and Why to Use the General Term of a Geometric Sequence Explain how to use the formula for the general term of a geometric sequence.
The Sum of the First n Terms of a Geometric Sequence Apply the formula used to find the sum of the first n terms in a geometric sequence.
Understand the Formula for Infinite Geometric Series Learn how to find the sum of an infinite geometric series using the proper formula.
How to Calculate a Geometric Series Differentiate between the formulas used to calculate infinite and finite geometric series.
Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences Explain the uses of recursion formulas for arithmetic, algebraic and geometric sequences.
Arithmetic and Geometric Series: Practice Problems Complete practice problems requiring you to use the correct formula for arithmetic and geometric series.
Using Sigma Notation for the Sum of a Series Use sigma notation to signify the sum of a series.
Mathematical Induction: Uses & Proofs Learn what mathematical induction is. Explore its uses to prove statements.
How to Find the Value of an Annuity Understand how to find the value of an annuity.
How to Use the Binomial Theorem to Expand a Binomial Apply the binomial theorem to expand a binomial and determine a specific term of a binomial expansion.
Special Sequences and How They Are Generated Find out how triangular numbers, tetrahedral numbers, cube numbers, square numbers and Fibonacci numbers are generated.

20 Lessons in Chapter 21: Mathematical Sequences and Series
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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