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12.3 Geometric Sequences and Series

12.3 Geometric Sequences and Series. ©2001 by R. Villar All Rights Reserved. Geometric Sequences and Series. Geometric Sequence: sequence whose consecutive terms have a common ratio. 1, 3, 9, 27, 81, 243, ... The terms have a common ratio of 3. The common ratio is the number r .

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12.3 Geometric Sequences and Series

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  1. 12.3 Geometric Sequences and Series ©2001 by R. Villar All Rights Reserved

  2. Geometric Sequences and Series Geometric Sequence: sequence whose consecutive terms have a common ratio. 1, 3, 9, 27, 81, 243, ... The terms have a common ratio of 3. The common ratio is the number r. Example Is the sequence geometric? 4, 6, 9, 13.5, 20.25, 30.375… Yes, the common ratio is 1.5 What is the 32nd term in this sequence? To find any term in a geometric sequence, use the formula an = a1 rn–1where r is the common ratio.

  3. Example: Find the twelfth term of the geometric sequence whose first term is 9 and whose common ratio is 1.2. an = a1 rn–1 a1 = 9 r = 1.2 a9 = 9 • 1.211 a12 = 66.87 To find the sum of a geometric series, we can use summation notation. Which can be simplified to:

  4. Example: Evaluate the sum of: Convert this to = 7.49952

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