Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April...
Transcript of Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April...
![Page 1: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/1.jpg)
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April 23, 2014
Sequences & Series Introduction
![Page 2: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/2.jpg)
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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?
![Page 3: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/3.jpg)
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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 :
![Page 4: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/4.jpg)
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Explicit Formula
• Formula that defines the nth term.
![Page 5: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/5.jpg)
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Write the first four terms of the sequence defined by the explicit formula :
n
t
![Page 6: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/6.jpg)
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Write the first four terms of the sequence defined by the explicit formula :
n
t
![Page 7: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/7.jpg)
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Write the first four terms of the sequence defined by the explicit formula :
n
t
![Page 8: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/8.jpg)
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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,
![Page 9: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/9.jpg)
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Write the first four terms of the sequence defined by the recursive formula :
n
t
![Page 10: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/10.jpg)
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Write the first four terms of the sequence defined by the recursive formula :
n
t
![Page 11: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/11.jpg)
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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?
![Page 12: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/12.jpg)
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Write a recursive formula for the sequence shown below and find the next three terms.
2, 8, 14, 20, 26, …
![Page 13: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/13.jpg)
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Write a recursive formula for the sequence shown below and find the next three terms.
7, 11, 15, 19, …
![Page 14: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/14.jpg)
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Write a recursive formula for the sequence shown below and find the next three terms.
2, 7, 22, 67,…
![Page 15: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/15.jpg)
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Write a recursive formula for the sequence shown below and find the next three terms.
5, 9, 17, 33….
![Page 16: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/16.jpg)
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Series
• Expression that indicates the sum of the terms of a sequence.
• We summation notation: Greek letter sigma
![Page 17: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/17.jpg)
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“the sum of 2n for values of n from 1 to 5”
![Page 18: Sequences & Series Introduction€¦ · Sequences & Series Introduction. Untitled.notebook 2 April 23, 2014 ... Write the terms of each series. Then evaluate. Untitled.notebook 19](https://reader036.fdocuments.in/reader036/viewer/2022081407/6053382770af3830cc3447aa/html5/thumbnails/18.jpg)
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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