Introducing Geometric Sequences
- Let’s explore growing and shrinking patterns.
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?
- 256, 128, 64
- 18, 54, 162
- 0.8, 0.08, 0.008
- 0.008, 0.08, 0.8
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|
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.
area of each shaded triangle
in square inches
0 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?
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.
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.