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Sequences

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What is a sequence? A list of numbers in a certain order. What is a term? One of the numbers in the sequence.

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What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. 4, 8, 12, 16, 20………….. +4

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What is the common difference? The difference between each number, or what you add each time. 4, 8, 12, 16, 20………….. 4 is the common difference How do you find it? The 2 nd term minus the 1 st term.

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Arithmetic Sequence Add the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is 2 50, 40, 30, 20… common difference is -10

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Arithmetic Sequences 4, 7, 10, 13,… –Common difference: + 3 27, 24, 21, 18,… –Common difference: - 3 5, 20, 35, 50,… –Common difference: + 15

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Arithmetic Sequences are Linear Patterns When you graph the pattern it makes a line Linear It goes up or down gradually.

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What is a geometric sequence? A sequence in which each term can be found by MULTIPLYING the previous term by the same number. 3, 9, 27, 81, 243………….. x3

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What is the common ratio? The ratio between each number in the sequence, or what you multiply by each time. 2, 8, 32, 128, 512………….. 4 is the common ratio How do you find it? The 2 nd term divided by the 1 st term.

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Geometric Sequence

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Geometric Sequences are Exponential Patterns When you graph the pattern it makes a steep curve Exponent ial It goes up or down fast!

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Make your own patterns 7.1 st term: 1, 2n 8.1 st term: 1000, 0.5n 9.1 st term: 3, 3n 10.1 st term: 390,625, 0.2n 11.1 st term: 1, 4n 12.1 st term: 100, 1.5n 1.1 st term: 1, n + 2 2.1 st term: 1000, n + (-50) 3.1 st term: 12, n + 6 4.1 st term: 81, n + (-9) 5.1 st term: 13, n + 5 6.1 st term: 20, n + (-4)

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Consecutive Terms: terms that are next to each other Variable Expression: can show the rule of a pattern Examples: 2, 4, 6, 8… n+2 8, 6, 4, 2… n + (-2) 2, 4, 8, 16… 2n16, 8, 4, 2… 0.5n

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Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference 1

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Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio

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What is the next term in this sequence? 5, 20, 80, 320, _____ 1,280 x4

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What is the next term in this sequence? 5, -1, -7 -13, _____ -19 -6

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What is the next term in this sequence? -3, 6, -12, 24, _____ -48 X-2

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What is the next term in this sequence? -400,-380,-360,-340, ____ -320 +20

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What is the next term in this sequence? 100, 75, 50, 25____ 0 -25

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What is the next term in this sequence? 12, -48, 192, -768____ 3,072 x-4

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Essential Skills: Identify and generate geometric sequences Relate geometric sequences to exponential functions 7-7: Geometric Sequences as Exponential.

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