©Evergreen Public Schools Learning Target 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 LaunchLaunch Do the table or graph represent a function? How do you know? function xy

©Evergreen Public Schools LaunchLaunch What is the domain and range of each function?domain and range xy

©Evergreen Public Schools LaunchLaunch Find 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 LaunchLaunch A n = 2, 6, 10, 14, … Sequences made with repeated addition are called arithmetic sequences. A n = 2, 6, 18, 54, … Sequences made with repeated multiplication are called geometric sequences.

©Evergreen Public Schools ExploreExplore

7 Kingdom of Montarek Growing, Growing, Growing p.7

©Evergreen Public Schools One day in the ancient kingdom of Montarek, a peasant saved the life of the 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 “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 The king replied, “Rubas are the least valuable coin in the kingdom. Surely you can think of a better reward.” But the peasant insisted, so the king agreed to her request. Did the peasant make a wise choice? Growing, Growing, Growing p.7

©Evergreen Public Schools 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 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 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 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 E. Which square will have 2 30 rubas? Explain. Growing, Growing, Growing p.7

©Evergreen Public Schools 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 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 Learning Target 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 Practice Practice 8.2A Generation Trees