Introducing Geometric Sequences: IM Alg2.1.2
[url=https://im.kendallhunt.com/HS/teachers/3/1/2/preparation.html]“Introducing Geometric Sequences”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.1.2 Lesson
- IM Alg2.1.2 Lesson: Introducing Geometric Sequences
- Alg2.1.2 Practice
- IM Alg2.1.2 Practice: Introducing Geometric Sequences
IM Alg2.1.2 Lesson: Introducing Geometric Sequences
What do you notice? What do you wonder?
[list][*]40, 120, 360, 1080, 3240[/*][*]2, 8, 32, 128, 512[/*][*]1000, 500, 250, 125, 62.5[/*][*]256, 192, 144, 108, 81[/*][/list]
Clare takes a piece of paper, cuts it in half, then stacks the pieces. She takes the stack of two pieces, then cuts in half again to form four pieces, stacking them. She keeps repeating the process.
The original piece of paper has length 8 inches and width 10 inches. Complete the table.
Describe in words how you can use the results after 5 cuts to find the results after 6 cuts.[br][br]
On the given axes, sketch a graph of the number of pieces as a function of the number of cuts.
How can you see on the graph how the number of pieces is changing with each cut?
On the given axes, sketch a graph of the number of pieces as a function of the number of cuts.
How can you see how the area of each piece is changing with each cut?
Clare has a piece of paper that is 8 inches by 10 inches.
How many pieces of paper will Clare have if she cuts the paper in half [math]n[/math] times?
What will the area of each piece be?
Why is the product of the number of pieces and the area of each piece always the same? Explain how you know.
Complete each geometric sequence. For each sequence, find its growth factor.
IM Alg2.1.2 Practice: Introducing Geometric Sequences
Here are the first two terms of a geometric sequence: 2, 4. What are the next three terms?
What is the growth factor of each geometric sequence?
1,1,1,1,1[br]
256, 128, 64[br]
18, 54, 162[br][br]
0.8, 0.08, 0.008[br]
0.008, 0.08, 0.8[br]
A person owes $1000 on a credit card that charges an interest rate of 2% per month. Complete this table showing the credit card balance each month if they do not make any payments.
[size=150]A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle. Starting from a single black equilateral triangle with an area of 256 square inches, here are the first four steps:[/size][br][img]data:image/png;base64,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[/img]
Complete this table showing the number of shaded triangles in each step and the area of each triangle.
Graph the number of shaded triangles as a function of the step number, then separately graph the area of each triangle as a function of the step number.
How are these graphs the same?
How are they different?
Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number.
Starting with the number 10, build a sequence of 5 numbers.[br]
Starting with the number 1, build a sequence of 5 numbers.[br]
Select a different starting number and build a sequence of 5 numbers.[br]
A sequence starts 1, -1,...
Give a rule the sequence could follow and the next 3 terms.[br]
Give a [i]different[/i] rule the sequence could follow and the next 3 terms.[br]