About This Chapter
Standard: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. (CCSS.Math.Content.HSA-SSE.B.4)
About This Chapter
Students who have mastered this standard are able to explain the importance of number patterns in mathematics. When working with sequences, they will be able to discern and explain the difference between the different types of sequences and series.
Lessons in this standard cover concepts such as:
- Finding and classifying arithmetic and geometric sequences
- Calculating arithmetic and geometric series
- Working with summation notation and mathematic series
Students demonstrate this standard when working with any set of numbers while attempting to find a pattern. An example of when mastery of this standard helps students is when they need to calculate mortgage payments.
How to Use These Lessons in Your Classroom
Here are some tips for how to use the lessons to support instruction in this standard:
Sequence Classification Lessons
Develop a worksheet that includes arithmetic and geometric sequences. Exhibit the video lessons 'How to Find and Classify an Arithmetic Sequence' and 'Finding and Classifying Geometric Sequences.' Pass out the worksheet to your students for homework. Spend the next day going over the correct answers and explain how each sequence is classified.
Summation Notation and Mathematical Series Lessons
Display the video lesson 'Summation Notation and Mathematical Series.' Give the students time to take our video lesson's supplementary quiz. After discussing each student's quiz score, take time to retake the quiz as a class while explaining how to find each answer.
Geometric and Arithmetic Series Calculation Lessons
In class, show the students the video lessons 'How to Calculate an Arithmetic Series' and 'How to Calculate a Geometric Series.' Assign the video lesson 'Arithmetic and Geometric Series: Practice Problems' for homework. During the next class, go over the assigned homework and have the class take the quizzes that we provide for each lesson.
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. 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.
4. 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!
5. 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.
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 Common Core Math - Algebra: High School Standards course
- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Equations
- Common Core HS Algebra: Linear Inequalities
- Common Core HS Algebra: Quadratics
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Rational and Radical Expressions and Equations
- Common Core HS Algebra: Systems of Equations
- Common Core HS Algebra: Matrices
- Understanding Common Core Standards