Lesson 2

Introducing Geometric Sequences

  • Let’s explore growing and shrinking patterns.

Problem 1

Here are the first two terms of a geometric sequence: 2, 4. What are the next three terms?

Problem 2

What is the growth factor of each geometric sequence?

  1. 1,1,1,1,1
  2. 256, 128, 64
  3. 18, 54, 162
  4. 0.8, 0.08, 0.008
  5. 0.008, 0.08, 0.8

Problem 3

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.

month total bill in dollars
1 1,000
2 1,020
3 1,040.40
4  
5  
6  
7  
8  

 

Problem 4

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:

A pattern of 4 congruent equilateral triangles. Starting with the first triangle, remove smaller congruent triangles to create the triangle to its right.
  1. Complete this table showing the number of shaded triangles in each step and the area of each triangle.
    step
    number    		 number of
    shaded triangles    		 area of each shaded triangle
    in square inches
    0 1 256
    1 3  
    2    
    3    
    4    
    5    
  2. 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.
  3. How are these graphs the same? How are they different?

Problem 5

Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number.

  1. Starting with the number 10, build a sequence of 5 numbers.
  2. Starting with the number 1, build a sequence of 5 numbers.
  3. Select a different starting number and build a sequence of 5 numbers.
(From Unit 1, Lesson 1.)

Problem 6

A sequence starts 1, -1, . . .

  1. Give a rule the sequence could follow and the next 3 terms.
  2. Give a different rule the sequence could follow and the next 3 terms.
(From Unit 1, Lesson 1.)