Name:
Class:
Topic:
Date:
Main Ideas/Questions:
Notes:
geometric
Sequences
Common
ratio
Identifying a
geometric
sequence
Determine whether the following represent geometric sequences. If so, identify the
common ratio.
1) 1, 5, 25, 125, 625…
2) 1, 3, 9, 12, 15…
3) 81, 27, 9, 3, 1…
4) -3, 6, -12, 24, -48…
5) -5, 5, -5, 5, -5…
6) 5, 15, 45, 135, 675…
Given the geometric sequence, find the next two terms.
7) 2, 6, 18, 54, ______, _______
Continuing
geometric
sequences
8) -4, 6, -9, 13.5, ______, _______
9) 96, 48, 24, 12, ______, _______
𝟓
10) 20, 10, 5, , ______, _______
𝟐
th
geometric The n term of an arithmetic sequence can be found using the
sequence following formula:
formula
Examples:
Write the rule
for the nth
term, then
find a66
11) 3, -6, 12, …
12) 3, 12, 48, … Main Ideas/Questions
Real Life
Application
Notes
13) -12, 12, -12, ….
14) 5, -15, 45, 5…
15) -208, -104, 52…
16) 11, -33, 99…
17) 𝟔𝟎. 𝟕𝟓, 𝟒𝟎. 𝟓, 𝟐𝟕 …
18) 192, -96, 48…
19) -32, -16, -8…
20) 𝟐 , 𝟒 , 𝟖 …
𝟏 𝟏 𝟏
1) Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it
rebounds to 85% of its previous height. How high will the ball rebound after its third
bounce? Round to the nearest tenth.
Name: _____________________________________ Unit 11: Relations and Functions
Date:_______________________
Class: ________ Homework 2: Geometric Sequences
Determine whether the following represent geometric sequences. If so, identify the common difference.
1. 1, 2, 6, 24, 120…
2. -12, 24, -48, 96, -192…
3. -1, -5, -25, -125, -625…
4. 60, 6, 0.6, 0.06, 0.006…
𝟓
𝟒
𝟐
𝟏
5. − 𝟑 , − 𝟑 , −𝟏, − 𝟑 , − 𝟑…
6. 4, 12, 36, 108, 324…
Given the Geometric Sequence, find the next two terms.
7. 2, 6, 18, _____, _____
8. 200, 100, 50, _____, _____
9. 10, 40, -160, _____, _____
10. -128, -64, -16, _____, _____
12. -7, 21, -63, _____, _____
11. 12, 18, 27, _____, _____
Write the rule for the nth term, and then find a7.
13. 2, 12, 72
14. 6, 24, 96
15. 4, -8, 16
16. -12, 12, -12
18. 128, 64, 32
17. 3, 12, 48