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©Evergreen Public Schools /31/2011 Geometric Sequences Teacher Notes Notes: Have students complete the sequence organizer in the debrief Vocabulary: geometric sequence common ratio

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Geometric Sequences Recursive Formula 2

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Math Practice 7 Target 3

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Math Practice 8 Target 4

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5 Learning Target A-SSE I can see structure in expressions. Identify and explain the initial value and common difference of an arithmetic sequence. Translate between sequences written in explicit form and recursive form.

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6 Learning Target F-IFa I can understand the concept of a function and use function notation. Recursive equations require the value of one term and it’s corresponding term number. Sequences can be defined by using either the next term or the previous term. The domain of sequences is the non-negative integers.

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7 Learning Target F-BF I can build a function. Write an explicit equation of an arithmetic or geometric sequence. Write a recursive equation of an arithmetic or geometric sequence.

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©Evergreen Public Schools LaunchLaunch From section SQ.1 What are the domains of the L ( x ) and a ( x ) sequences?

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©Evergreen Public Schools LaunchLaunch From section SQ.2 Rumors What is the domains of the rumors?

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©Evergreen Public Schools LaunchLaunch What do you think is true about the domain of any sequence?

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©Evergreen Public Schools ExploreExplore

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©Evergreen Public Schools Sequences a) 3, 6, 9, 12, 15, … b) 3, 6, 12, 24, 48, … 1.What do the sequences have in common? 2.How are they different? 3.Write an explicit rule with sequence notation for each.

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©Evergreen Public Schools Arithmetic Sequences L(x) = 2x + 1 and N(x) = 34 – 4x are arithmetic sequences. They have a constant rate of change. What is the rate of change of L(x) and N(x)?

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©Evergreen Public Schools Sequences The sequence in the Rumors problem is a geometric sequence. It does not have a constant rate of change. Describe the data of change of the Rumors problem.

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©Evergreen Public Schools Geometric Sequences The sequences that are generated by repeated multiplication are called geometric sequences. b)3, 6, 12, 24, 48, … from slide 12 is an example.

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©Evergreen Public Schools Geometric Sequences b)3, 6, 12, 24, 48, … from slide 12 is an example. Look for a pattern in ratio of consecutive terms Since the ratio is the same, we call it the common ratio.

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©Evergreen Public Schools Equations of Geometric Sequences We found the equations for the Rumors problem is b) What is the equation for 3, 6, 12, 24, …

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©Evergreen Public Schools Find next term and write equation with sequence notation. I 1, -10, 100, -1000, … II 5, 10, 20, 40, … III 4, 12, 36, 108, IV 64, 16, 4, 1, …

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©Evergreen Public Schools Find next term and write equation with sequence notation. III -243, -81, -27, -9, … IIIIV 4, 6, 9, 13.5

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©Evergreen Public Schools r = common ratio In explicit form a n = n = term number In recursive form a n = and a n+1 = and

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©Evergreen Public Schools Team Practice

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©Evergreen Public Schools Debrief Complete the sequence organizer for geometric sequences.

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©Evergreen Public Schools Learning Target Did you hit the target? Sequences 3a I can write an equation of a geometric sequence in explicit form. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

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©Evergreen Public Schools Practice KUTA Geometric Sequences Worksheet.

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©Evergreen Public Schools Write the equation for the sequences with sequence notation in explicit form. 1)11, 22, 44, 88,... 2)128, 64, 32, 16, …

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