# 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:

1. Complete this table showing the number of shaded triangles in each step and the area of each triangle.
step
number
number of
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.)