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©Evergreen Public Schools
2010
1
Target 12 Level 3
I can write an equation of a geometric sequence in explicit form.
I can identify the domain and range of a geometric sequence.
What is domain? What is range?
©Evergreen Public Schools
2010
2
LaunchLaunchLaunchLaunchDo the table or graph represent a
function? How do you know?
x y
-2 6
0 4
2 7
5 6
12 -1
©Evergreen Public Schools
2010
3
LaunchLaunchLaunchLaunchWhat is the domain and range of each
function?
x y
-2 6
0 4
2 7
5 6
12 -1
©Evergreen Public Schools
2010
4
LaunchLaunchLaunchLaunchFind a rule to fit the sequence.
1. f(x) = 2, 6, 10, 14, …
2. g(x) = 2, 6, 18, 54, …
How are the sequences alike?
How are they different?
©Evergreen Public Schools
2010
5
LaunchLaunchLaunchLaunchAn = 2, 6, 10, 14, …
Sequences made with repeated addition are called arithmetic sequences.
An = 2, 6, 18, 54, …
Sequences made with repeated multiplication are called geometric sequences.
©Evergreen Public Schools
2010
6
©Evergreen Public Schools
2010
7
Kingdom of Montarek
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
8
One day in the ancient kingdom of Montarek, a peasant saved the life ofthe king’s daughter. The king was so grateful he told the peasant she could have any reward she desired.
The peasant—who was also the kingdom’s chess champion—made an unusual request:
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
9
“I would like you to place 1 ruba on the first square of my chessboard,2 rubas on the second square, 4 on the third square, 8 on the fourth square, and so on, until you have covered all 64 squares. Each square should have twice as many rubas as the previous square.”
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
10
The king replied, “Rubas are the least valuable coin in the kingdom. Surelyyou can think of a better reward.” But the peasant insisted, so the kingagreed to her request.
Did the peasant make a wise choice?
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
11
A. 1. Make a table showing the number of rubas the king will place on squares 1 through 10 of the chessboard.
2. How does the number of rubas change from one square to the next?
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
12
B. Here’s the graph for squares 1 to 6. (number of the square, number of rubas)
a)Should the points be connected?
b)Is the graph a function?
c)What is the domain of the function?
d)What is the range of the function?
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
13
C. Write an equation for the relationship between the number of the square n and the number of rubas, r.
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
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D. How does the pattern of change you observed in the table show up in the graph?
How does it show up in the equation?
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
15
E. Which square will have 230 rubas?
Explain.
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
16
F. What is the first square on which the king will place at least one million rubas?
How many rubas will be on this square?
Growing, Growing, Growing p.7
©Evergreen Public Schools
2010
17
Placemat Placemat
Write your response to one of the questions on your section of the placemat:
• What do you understand about geometric sequences?
• What questions do you have about arithmetic sequences?
Name 1
Name 2
Name 3
Name 4
©Evergreen Public Schools
2010
18
5
3
12
4
Did you hit the target?
I can write an equation of a geometric sequence in explicit form.
I can identify the domain and range of a geometric sequence.
©Evergreen Public Schools
2010
19
PracticePractice
Practice 8.2A Generation Trees
