Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April...
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Untitled.notebook 1 April 23, 2014 Sequences & Series Introduction
Transcript of Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April...
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Sequences & Series Introduction
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The petals of a flower are as follows:
1, 1, 2, 3, 5, 8, 13, …
Can you find the next four values?
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Sequence• An ordered list of numbers called Terms
• Infinite Sequence – continues without end.
• Finite Sequence – has a last term
• Terms represented by t :
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Explicit Formula
• Formula that defines the nth term.
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Write the first four terms of the sequence defined by the explicit formula :
n
t
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Write the first four terms of the sequence defined by the explicit formula :
n
t
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Write the first four terms of the sequence defined by the explicit formula :
n
t
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Recursive Formula• One or more previous terms are
used to generate the next term.
• Find the next three terms:• 4, 7, 10, 13, 16,
• 2, 6, 18, 54,
• 1, 4, 9, 16,
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Write the first four terms of the sequence defined by the recursive formula :
n
t
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Write the first four terms of the sequence defined by the recursive formula :
n
t
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Back to the petals of a flower:
1, 1, 2, 3, 5, 8, 13, …
Can you write a recursive formula for this?
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Write a recursive formula for the sequence shown below and find the next three terms.
2, 8, 14, 20, 26, …
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Write a recursive formula for the sequence shown below and find the next three terms.
7, 11, 15, 19, …
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Write a recursive formula for the sequence shown below and find the next three terms.
2, 7, 22, 67,…
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Write a recursive formula for the sequence shown below and find the next three terms.
5, 9, 17, 33….
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Series
• Expression that indicates the sum of the terms of a sequence.
• We summation notation: Greek letter sigma
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“the sum of 2n for values of n from 1 to 5”
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Write the terms of each series. Then evaluate.
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Write the terms of each series. Then evaluate.
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Homework
