Chapter 14 Sequences Series and the Binomial Theorem
Chapter 14 Sequences, Series, and the Binomial Theorem Section 3 Geometric Sequences & Series Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 1
Study Strategy Study Groups üTaking the Test and Anxiety Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2
Concept Geometric Sequences A geometric sequence is a sequence in which each term, after the first term, is a constant multiple of the preceding term. This means that the general term is for The number r is called the common ratio of the geometric sequence. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3
Example Geometric Sequences Find the first 5 terms of a geometric sequence whose first term is 8 and whose common ratio is 3. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4
Example Geometric Sequences Find the common ratio for the geometric sequence: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5
Concept General Term of a Geometric Sequence If a geometric sequence whose first term is a 1 has a common ratio of r, then the general term of this sequence is Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6
Example General Term of a Geometric Sequence Find the general term of the geometric sequence: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7
Concept Geometric Series A geometric series is the sum of the terms of a geometric sequence. A finite geometric series consists of only the first n terms of a geometric sequence, and is denoted as sn. The sum of the first n terms of a geometric sequence is given by where a 1 is the first term of the sequence and r is the common ratio of the sequence. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8
Example Geometric Series Find s 8 for the geometric sequence: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 9
Concept Infinite Geometric Series For a geometric sequence has a common ratio r such that then the infinite geometric series has a limit, and this limit is given by the formula If then no limit exists. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10
Example Infinite Geometric Series (page 1) Find s for the geometric sequence: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11
Example Infinite Geometric Series (page 2) Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 12
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