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12.1 – Arithmetic Sequences and Series

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An introduction………… Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms Geometric Series Sum of Terms

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Find the next four terms of –9, -2, 5, … Arithmetic Sequence 7 is referred to as the common difference (d) Common Difference (d) – what we ADD to get next term Next four terms……12, 19, 26, 33

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Find the next four terms of 0, 7, 14, … Arithmetic Sequence, d = 7 21, 28, 35, 42 Find the next four terms of x, 2x, 3x, … Arithmetic Sequence, d = x 4x, 5x, 6x, 7x Find the next four terms of 5k, -k, -7k, … Arithmetic Sequence, d = -6k -13k, -19k, -25k, -32k

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Vocabulary of Sequences (Universal)

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Given an arithmetic sequence with x NA -3 X = 80

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?? x 6 353

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Try this one: x NA 0.5

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9 x 633 NA 24 X = 27

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NA x

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Find two arithmetic means between –4 and 5 -4, ____, ____, NA x The two arithmetic means are –1 and 2, since –4, -1, 2, 5 forms an arithmetic sequence

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Find three arithmetic means between 1 and 4 1, ____, ____, ____, NA x The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence

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Find n for the series in which 5 x y X = 16 Graph on positive window

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12.2 – Geometric Sequences and Series

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Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms Geometric Series Sum of Terms

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Vocabulary of Sequences (Universal)

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Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic

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1/2 x 9 NA 2/3

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Find two geometric means between –2 and 54 -2, ____, ____, NA x The two geometric means are 6 and -18, since –2, 6, -18, 54 forms an geometric sequence

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-3, ____, ____, ____

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x 9 NA

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x 5

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*** Insert one geometric mean between ¼ and 4*** *** denotes trick question 1/4 3 NA

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1/2 7 x

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Section 12.3 – Infinite Series

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1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2, 4, 8, …Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

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Find the sum, if possible:

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The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. How far does the ball travel? / /5

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The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. How far does the ball travel? / /4

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Sigma Notation

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UPPER BOUND (NUMBER) LOWER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE)

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Rewrite using sigma notation: Arithmetic, d= 3

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Rewrite using sigma notation: Geometric, r = ½

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Rewrite using sigma notation: Not Arithmetic, Not Geometric

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Rewrite the following using sigma notation: Numerator is geometric, r = 3 Denominator is arithmetic d= 5 NUMERATOR: DENOMINATOR: SIGMA NOTATION:

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