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Sequences & Series

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Sequences A sequence is a function whose domain is the set of all positive integers. The first term of a sequences is denoted a 1 The second term of a sequences is denoted a 2 The nth term of a sequence is denoted a n

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Arithmetic Sequences A sequence that is obtained by adding a constant d to the previous term. Give the next 3 terms. What’s being added repeatedly (d)?

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Generating Sequences Give the first 4 terms of the arithmetic sequence whose first term is 12 with a common difference 7. Give the first 4 terms of the arithmetic sequence whose first term is 241 with a common difference –31. 12, 19, 26, 33 241, 210, 179, 148

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Generating Sequences Give the first 4 terms of the sequence. 5, 8, 11, 14 5, 11, 17, 23

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Arithmetic Means The missing terms of an arithmetic sequence are called arithmetic means. Find the missing terms of the following arithmetic sequence. 11,,, 38, … 16,,,, -24, … 2029 6-14-4

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Definitions/Rules Write a rule for the following arithmetic sequence. 5, 7, 9, 11, 13, … What’s the first term? What’s the common difference? Plug into formula.

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Geometric Sequences A sequence that is obtained by multiplying the common ratio r to the previous term. Give the next 3 terms. What’s being multiplied repeatedly?

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Generating Sequences Give the first 4 terms of the geometric sequence whose first term is 3 and with a common ratio 4. Give the first 4 terms of the geometric sequence whose first term is -2 and with a common ratio -3. 3, 12, 48, 192 -2, 6, -18, 54

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Generating Sequences Give the first 4 terms of the geometric sequence. 5, 10, 20, 40

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Geometric Means The missing terms of a geometric sequence are called geometric means. Find the missing terms of the following geometric sequence. 6,,, 162,… -1,,,, -625, … 1854 -5 or +5-25 -125 or +125

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Definitions/Rules Write a rule for the following geometric sequence. 1, 4, 16, 64, … What’s the first term? What’s the common ratio? Plug into formula.

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Series A series is the sum of terms of a sequence. Summation (Sigma) Notation is used. Starting value to plug in Ending value to plug in The function used 56

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Evaluate the Series

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