2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences...
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Transcript of 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences...
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2-3 Geometric Sequences
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1Definitions & Equations
Writing & Solving Geometric Sequences
Practice Problems
![Page 2: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/2.jpg)
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Definitions
Geometric Sequence A sequence in which each term after
the first is found by multiplying the previous term by a constant
Common Ratio (r) The constant each term is multiplied
by in a geometric sequence
![Page 3: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/3.jpg)
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nth Term of an Geometric Sequence
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nna a r
1nn
ara
![Page 4: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/4.jpg)
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Finding the Next Term
Find the next term in the geometric sequence: 8, 20, 50, 125, ?
1nn
ara
1252.5
50r
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nna a r
5 18 2.5na
312.5na
![Page 5: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/5.jpg)
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Finding a Particular Term
Find the eighth term of a geometric sequence for which a1 = -3, and r = -2
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nna a r
8 18 ( 3) ( 2)a
8 384a
![Page 6: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/6.jpg)
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Write an Equation for the nth Term
Write an equation for the nth term of the geometric sequence 3, 12, 48,192…
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nna a r
1nn
ara
124
3r
13 4nna
![Page 7: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/7.jpg)
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Find a Term Given the Fourth Term and the Ratio
Find the tenth term of a geometric sequence for which a4 = 108, and r = 3
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nna a r
4 14 1 3a a
1108 27a
14 a
10 110 4 3a
10 4 19683a
10 78,732a
![Page 8: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/8.jpg)
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Finding Geometric Means
Find three geometric means between 2.25 and 576.1
1n
na a r 1
5 1na a r
5 1576 2.25 r 4576 2.25 r
4256 r4 r
2 12 2.25 4 9a
3 13 2.25 4 36a
4 14 2.25 4 144a
![Page 9: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/9.jpg)
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Practice Problems
![Page 10: 2-3 Geometric Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Sequences Practice Problems.](https://reader036.fdocuments.net/reader036/viewer/2022082710/56649dc35503460f94ab512c/html5/thumbnails/10.jpg)
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Practice Problems