2-3 Geometric Sequences

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1Definitions & Equations

Writing & Solving Geometric Sequences

Practice Problems

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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

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nth Term of an Geometric Sequence

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nna a r

1nn

ara

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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

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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

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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

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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

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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

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Practice Problems

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Practice Problems