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31 Cards in this Set
- Front
- Back
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When is your next quiz?
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Tuesday!
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sequence
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commonly thought of as a pattern of numbers,. but we can also think of a sequence as a function whose domain consists of consecutive natural numbers
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natural numbers
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{1,2,3,4,5,...} Each corresponding value in the range is called a term in the sequence
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arithmetic sequence
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linear functions, there is a common number is added to the sequence is the slope, or rate of change, of the linear function
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Geometric Sequences
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multiply
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Arithemetic Sequences
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add and subtract
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31, 36, 41, 46, 51
What is the first term? What is the 3rd term? What is the common difference? |
31
third term-41 Common difference +5 |
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n as we are learning has to be a _________ number.
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whole
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0,1,2,3,4,5,6,7,8
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whole numbers
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sequence
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an ordered list of numbers, pictures, letters, geometric figures, or just about any object you like
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term
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the objects, numbers, figure, in sequence.
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whole numbers
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0,1,2,3,4,
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terms are separated by
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commas
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input or domain are going to be
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whole numbers
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whole numbers do not include
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fractions and negative number
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Some sequence follow _______ patterns.
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predictable
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Some sequences have no _________ at all.
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pattern
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finite sequences
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they contain a finite number of terms
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infinite sequences
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they contain an infinite number of terms
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ellipses
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the three dots that indicate that some of the terms are missing.
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necessary for infinite sequences
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ellipses
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also used for large finite sequences too
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ellipses
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using ______ allpows us to indicate the sequence without having to write all of the numbers
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ellipses
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In looking for ______ in sequences it is useful to look for a pattern in how each term relates to the previous term.
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patterns
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4, 7, 10, 13, 16
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infinite sequence
arithmetic (We added 3 to get the next term-this is how each term "relates" to the other) |
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1, 2, 3, 4, 5,...,999, 1000
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finite sequence
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arithmetic sequences
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find the common difference by subtracting
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geometric sequences
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find common ration out by dividing
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To find a term, we use the formulas that we have already
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memorized
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recursive definition
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definition for the sequence that gives the first term and a formula for how the nth term relates to the (n-1)th term
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1,2,3,4,5,...What is the first term?
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1
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