# 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
- 256, 128, 64
- 18, 54, 162
- 0.8, 0.08, 0.008
- 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:

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

numbernumber of

shaded trianglesarea of each shaded triangle

in square inches0 1 256 1 3 2 3 4 5 - 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?

### Problem 5

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.
- Starting with the number 1, build a sequence of 5 numbers.
- Select a different starting number and build a sequence of 5 numbers.

### Problem 6

A sequence starts 1, -1, . . .

- Give a rule the sequence could follow and the next 3 terms.
- Give a
*different*rule the sequence could follow and the next 3 terms.