Transcription of 8.3 Analyzing Geometric Sequences and Series
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8.3 Analyzing Geometric Sequences and Series
Section Analyzing Geometric Sequences and Series 425 Essential QuestionEssential Question How can you recognize a Geometric sequence from its graph?In a Geometric sequence , the ratio of any term to the previous term, called the common ratio, is constant. For example, in the Geometric sequence 1, 2, 4, 8, .. , the common ratio is 2. Recognizing Graphs of Geometric SequencesWork with a partner. Determine whether each graph shows a Geometric sequence . If it does, then write a rule for the nth term of the sequence and use a spreadsheet to fi nd the sum of the fi rst 20 terms. What do you notice about the graph of a Geometric sequence ?a. nan812164462 b. nan812164462c. nan812164462 d. nan812164462 Finding the Sum of a Geometric SequenceWork with a partner. You can write the nth term of a Geometric sequence with fi rst term a1 and common ratio r asan = a1r n , you can write the sum Sn of the fi rst n terms of a Geometric sequence asSn = a1 + a1r + a1r 2 + a1r 3 +.
Section 8.3 Analyzing Geometric Sequences and Series 425 EEssential Questionssential Question How can you recognize a geometric sequence from its graph? In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant.For example, in the geometric sequence 1, 2, 4, 8, . . .
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