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Unit 1 is all about finding patterns when given sequences. Whether the sequence given is a diagram or a list of numbers, we can use it to find an equation, create a table, and create a graph.
Arithmetic sequences involve a constant difference between consecutive terms, while geometric sequences have a constant ratio between terms. We will learn how to identify these sequences, find their common difference or ratio, and determine their terms.
Throughout the unit, we will also explore the applications of arithmetic and geometric sequences in fields such as finance, population growth, and more. This knowledge will not only enhance your mathematical skills but also equip you with practical problem-solving abilities.
Lesson 1
Lesson 1 is all about looking for patterns in diagrams. In the videos, you will explore the concept of looking for patterns in growing diagrams and how they can help us understand and predict growth in various scenarios.
Visual Pattern- Writing an Equation and Creating a Table
Visual Pattern- Writing an Equation and Creating a Table
Visualizing Patterns
Visualizing Patterns
Lesson 2
Lesson 2 is all about creating new representations of the patterns that we find in diagrams and sequences. We are going to do this using tables, graphs, and two different types of equations. The sequences we looked at in Lesson 2 are all Arithmetic Sequences. This means that from one figure to the next, the same amount is being added or subtracted each time. We call this amount the Common Difference
Linear: Growth Patterns
Linear: Growth Patterns
Nth Term Arithmetic Sequence
Nth Term Arithmetic Sequence
Explicit & Recursive Formulas Arithmetic
Explicit & Recursive Formulas Arithmetic
Graphing Arithmetic Sequences
Graphing Arithmetic Sequences
Lesson 3
Lesson 3 is where we learn about a new type of sequence, geometric. Geometric is different from Arithmetic because it is no longer adding or subtracting, but it is multiplying. We will once again learn about how to write equations, make tables, and create graphs for these sequences.
Identifying geometric sequences and finding the common ratio
Identifying geometric sequences and finding the common ratio
Explicit & Recursive Formulas Geometric Sequences
Explicit & Recursive Formulas Geometric Sequences
Writing and Graphing Geometric Sequences
Writing and Graphing Geometric Sequences
Lesson 4
Lesson 4 is a practice lesson for us to get used to writing Recursive and Explicit equations when given a diagram and a scenario. Here are some example videos to help you.
Writing and Using Recursive and Explicit Rules for Arithmetic Sequences
Writing and Using Recursive and Explicit Rules for Arithmetic Sequences
Explicit and Recursive Rules for Arithmetic Sequences
Explicit and Recursive Rules for Arithmetic Sequences
Lesson 5
Lesson 5 is about making different representations (tables, graphs, and equations) when given a Geometric Sequence in the form of a story problem. When we see story problems, it's important to highlight the things that we know and what we think is going to be important. Then we can take the next steps to completing the problem.
Geometric Sequence Word Problems
Geometric Sequence Word Problems
Geometric Sequence Word Problems
Geometric Sequence Word Problems
Lesson 6
Lesson 6 is when we learn about Decreasing sequences. Some of the videos on this page already have, but we haven't in class yet. Decreasing arithmetic sequences are using subtraction, and you would think the decreasing geometric sequences use division, but that is incorrect. Geometric sequences only use multiplication, even when the decrease. If you multiply by a number that is between 0 and 1, you will notice a decrease.
In this lesson we also work with percentages for the first time. Anytime we see a percentage, we know it is a geometric sequence. There are a couple extra steps to do when we are given a percentage, so I have included some videos about that as well.
Nth Term of a decreasing sequence (Arithmetic)
Nth Term of a decreasing sequence (Arithmetic)
Decreasing Geometric Sequences
Decreasing Geometric Sequences
Percent Increase, Geometric Sequence Word problem
Percent Increase, Geometric Sequence Word problem
Sequences: Percentage Increase and Decrease
Sequences: Percentage Increase and Decrease
Lesson 7
Geometric, Arithmetic, or Neither? That is what we are exploring in this lesson. It is your job to figure out if a sequence of numbers is Geometric (multiplying), Arithmetic (adding/subtracting) or Neither (literally anything else). You will also need to be able to identify the common ratios and common difference of different sequences along with writing recursive and explicit equations. It's a lot, I know, but you've done it all before. This lesson shouldn't be brand new to you, and if it is, I would suggest watching some previous videos.
Percent Increase, Geometric Sequence Word problem
Percent Increase, Geometric Sequence Word problem
How to determine if a sequence is arithmetic or geometric
How to determine if a sequence is arithmetic or geometric
Lessons 8 and 9
Now we are going to get a little tricky. What if I were to give you a sequence that was missing numbers? Could you find those numbers? Hopefully after watching these videos you can. Lesson 8 focuses on Arithmetic Sequences, while Lesson 9 focuses on Geometric Sequences.
Finding Missing Terms of Arithmetic Sequences
Finding Missing Terms of Arithmetic Sequences
How to Find Missing Terms Geometric
How to Find Missing Terms Geometric
Lesson 10
Our final lesson of Unit 1 is all about Practicing what we have learned. You won't learn anything new in this lesson, but you should be working towards fluency (getting really good). So I have compiled a few more videos that focus on equations and a bunch of practice sites on Khan Academy for you to keep preparing for the test.
“Don’t practice until you get it right, practice until you never get it wrong.” -John Flanagan
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