1. Check it out!
2.5.1: Geometric Sequences

2. What was the height of the ball after the first bounce?
Alicia’s little sister found a tennis ball at the playground. Her sister then climbed to the top of the jungle gym and dropped the ball from a height of 10 feet. With each new bounce, the ball reached only 40% of the height of the previous bounce.
What was the height of the ball after the first bounce?
What was the height of the ball after the second bounce?
What was the height of the ball after the third bounce?
What was the height of the ball after the fourth bounce?
Graph the number of bounces versus the height of each bounce in feet.
Does the graph show a pattern? Explain.
Common Core State Standard: MCC9–12.A.SSE.4★
2.5.1: Geometric Sequences

3. What was the height of the ball after the first bounce?
To determine the height after the first bounce, find 40% of 10 feet.
0.40(10) = 4
The ball was 4 feet high after the first bounce.
2.5.1: Geometric Sequences

4. What was the height of the ball after the second bounce?
To determine the height after the second bounce, find 40% of the previous bounce height, 4 feet.
0.40(4) = 1.6
The ball was 1.6 feet high after the second bounce.
2.5.1: Geometric Sequences

5. What was the height of the ball after the third bounce?
To determine the height after the third bounce, find 40% of the previous bounce height, 1.6 feet.
0.40(1.6) = 0.64
The ball was 0.64 feet high after the third bounce.
2.5.1: Geometric Sequences

6. What was the height of the ball after the fourth bounce?
To determine the height after the fourth bounce, find 40% of the previous bounce height, 0.64 feet.
0.40(0.64) = 0.256
The ball was feet high after the fourth bounce.
2.5.1: Geometric Sequences

7. Graph the number of bounces versus the height of each bounce in feet.
2.5.1: Geometric Sequences

8. Does the graph show a pattern? Explain.
Yes, the graph shows that the bounce height decreases by 40% with each successive bounce.
Connection to the Lesson
Students will continue to work with exponential functions as geometric sequences.
Students will review what a geometric sequence is and how to write sequences using formulas.
2.5.1: Geometric Sequences