Math 20-1

Chapter 1 Sequences and Series

Lesson 1.4    Geometric Series

Support Documents

Answer pages

You should be checking your work for EVERY question you do!

To make that easy, you can download the solutions files which have the answers for all the practice problems in the text.

You can print it, though it would be a lot of pages.

I think the best choice would be to keep the files handy, and have them open and ready every time you are working on math.

This saves you the time of flipping to the back of the book every time you need to check an answer.

FOLDER LINK

Formula Page

Math 20-1 is an academic course and you will be expected to memorize a lot of what you are covering in class.

Your teacher will have expectations for the things you will see on a formula page.

The link below is to formula page that you can download and print to use with your course.

You may or may not be allowed to use this on tests, and you may or may not be allowed to ADD your own notes to these pages.

Use of this page depends on your teacher.

What goes on this page is also subjective, so it is subject to change!

Formula Page

Focus on...

Lesson Objectives

•	deriving a rule for determining the sum of n terms of a geometric series

•	determining  (Subscript[t, 1]), r, n or (Subscript[S, n])  involving a geometric series

•	solving a problem that involves a geometric series

•	identifying any assumptions made when identifying a geometric series

Focus on...  Activity

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 46

Read/Work through the  Focus  section at the top of page 46 in  your textbook.

Do your best to answer the questions given in this section.
These ideas will all be covered in the lesson.
(you can use the demonstration found in the next section to explore the ideas of this activity

Video Tutorial  A

Not sure how well this page will work for you,  and you might need a pretty powerful computer, but THIS SITE has an amazing fractal image that will illustrate the idea of “self similarity”.
You can zoom in and out of the page, wait for it to refresh...you can see the “motif” of the circular shape with the curley-cues coming out of it...

Demonstration

Investigate  Fractals

The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 46 - 47

Read/Work through the  Investigate  section on Pages 46 - 47 in your textbook.

A list of materials  you need for the Investigation is given in the side bar.

Your work will be a lot more efficient if you PLAN for and GATHER these items BEFORE you start the Investigation!

You may not have other students to work with.  
No worries!  
If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Tutorial that follows.
Once you have done that,  view the video  content for help with this section.

Video Tutorial  B

Video Tutorial  C

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Pages 48 - 49

Read/Work through the  Link the Ideas  section on Pages 48 - 49 in your textbook.

I suspect that MOST students will not really be all that interested in the quite difficult derivation of the formula for the sum of a geometric series.

If you really need this,  let me know, I’ll happily make the video!

You don’t need to know the derivation to be able to use the formula.

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1  Determine the Sum of a Geometric Series

TEXT Pages 49 - 50

Work through Example 1 on Pages 49 - 50 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Determine the Sum of a Geometric Series for an Unspecified Number of Terms

TEXT Pages 50 - 51

Work through Example 2 on Pages 50 - 51 in your textbook.

Watch

Video Tutorial develop a formula

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Apply Geometric Series

TEXT Page 52

Work through Example 3 on Page 52 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Key Ideas

Key Ideas summarizes the main new concepts of the lesson.

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Check Your Understanding    (Practice Problems)

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Practice 
These questions allow you to check your understanding of the concepts. 
You can often do the first few questions by checking the Link the Ideas notes or by following one of the worked Examples.

Apply 
These questions ask you to apply what you have learned to solve problems. 
You can choose your own methods of solving a variety of problem types.

Extend 
These questions may be more challenging. 
Many connect to other concepts or lessons. 
They also allow you to choose your own methods of solving a variety of problem types.

Create Connections
These questions focus your thinking on the Key Ideas and also encourage communication. 
Many of these questions also connect to other subject areas or other topics within mathematics.

Mini Lab
These questions provide hands-on activities that encourage you to further explore the concept you are learning.

Notes

Question 12, you can use the demonstration below to experiment with the Koch “snowflake”

Question 13,    The textbook interprets this question differently than I did  (not saying I am right!)
They used a first term of 1400 and I used a first term of 1000...
Not quite sure I understand their reasoning....

Question 21,    I didn’t do a video for this one.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14", "Question 15"}, {"Question 16", "Question 17", "Question 18", "Question 19", }})

({{"CC 20",  , "CC 22"}})