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Published byBathsheba Avice Harmon Modified over 8 years ago

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CN College Algebra Ch. 11: Sequences 11.3: Geometric Sequences Goals: Determine if a sequence is geometric. Find a formula for a geometric sequence. Find the sum of a geometric sequence. Find the sum of a geometric series.

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Geometric Sequences: Geometric Sequence: When the ratio of successive terms of a sequence is always the same nonzero number, the sequence is called geometric. A geometric sequence may be defined recursively as where a = a 1, and r ≠ 0 are real numbers. The number a is the first term, and the nonzero number r is called the common ratio.

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Geometric Sequence Theorems: Theorem – n th Term of a Geometric Sequence: For a geometric sequence {a n } whose first term is a and whose common ratio is r, the n th term is determined by the formula Theorem – Sum of n Terms of a Geometric Sequence: Let {a n } be a geometric sequence with first term a and common ratio r, where r ≠ 0, r ≠ 1. The sum S n of the first n terms of {a n } is

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Geometric Series: Geometric Series: An infinite sum of the form with first term a and common ratio r, is called an infinite geometric series and is denoted by Sum of an infinite geometric series: The sum S n of the first n terms of a geometric series is If this finite sum Sn approaches a number L as n , then we call L the sum of the infinite geometric series and we write

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Sum of an Infinite Geometric Series: Theorem – Sum of an Infinite Geometric Series: If |r| < 1, the sum of the infinite geometric series is

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Assignments: Class work: Sequences and Series worksheet. Homework: 11.3 Exercises #1-5 (odds), 11-21 (odds), 25-29 (odds), 33, 39, 41, 71.

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