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©Evergreen Public Schools 2011 1 4/11/2011 Arithmetic Sequences Explicit Rules Teacher Notes Notes : We will continue work students have done with arithmetic sequences. Vocabulary : arithmetic sequence explicit form

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©Evergreen Public Schools 20102 Practice Target Practice 7: Look for and make use of structure. Practice 7: Look for and make use of structure. Practice 8: Look for and express regularity in repeated reasoning.

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©Evergreen Public Schools 2011 3 Learning Target Sequences 2 I can write an equation and find specific terms of an arithmetic sequence in explicit form.

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©Evergreen Public Schools 2011 4 LaunchLaunch 1. Complete the table and write an equation to find the area of L ( x ).

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©Evergreen Public Schools 2011 5 ExploreExplore

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6 Find the next 3 terms. Explain why it is or is not arithmetic. I.5, 8, 11, 14, ____, ____, ____, … II.3, 6, 12, 24, ____, ____, ____, … III.24, 19, 14, ____, ____, ____, … IV.2, 3, 5, 8, 12, ____, ____, ____, … Which are arithmetic sequences?

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Sequence Notation L ( x ) is function notation L(1) is the first term of the function. L n is sequence notation. L 1 is the first term of the sequence Question: How is sequence notation similar to function notation?

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©Evergreen Public Schools 2011 8 Write rule and terms for each of the sequences SequenceTermsEquation a n = 4, 7, 10, 13, …a5 =a8 =a5 =a8 = a n = 8, _____, 20, 26, …a 2 = a 10 = a n = ___, 30, 26, ___, …a1 =a4 =a8 =a1 =a4 =a8 =

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©Evergreen Public Schools 2011 9 Team Practice 1.Find the explicit formula for 15, 12, 9, 6,... 2.Find the explicit formula for 5, 9, 13, 17, 21,... 3.Find a 10, a 35 and a 82 for problem #2. 4.Find the explicit formula when a 1 = 6 and rate of change = 2. 5.Find a 10, a 35 and a 82 for problem #4. 6.Is 327 a term in the sequence 8, 13, 18,...?

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©Evergreen Public Schools 2011 10 5 3 1 2 4 Learning Target Did you hit the target? Sequences 2 I can write an equation and find specific terms of an arithmetic sequence in explicit form.

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©Evergreen Public Schools 2011 11 Practice

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©Evergreen Public Schools 2011 12 A n = 4( n – 1) + 7 Find A 10

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