ch.13 Sequences and Series

ch.13 Sequences and Series - Chapter 13 Sequences and...

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Chapter 13 Sequences and Series 13.1 Sequences
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Key Points Definition of a sequence Arithmetic and geometric sequences
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Sequences Examples Finite infinite Notation
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Notation for Sequences and Examples We denote the terms of a sequence by a 1 , a 2 , a 3 , . . . , a n , . . . so that a 1 is the first term, a 2 is the second term, and so on. We use a n to denote the nth or general term of the sequence. If there is a pattern in the sequence, we may be able to find a formula for a n . Example 1 (a) 0, 1, 4, 9, 16, 25, . . . is the sequence of squares of integers. (b) 2, 4, 8, 16, 32, . . . is the sequence of positive integer powers of 2. (c) 3, 1, 4, 1, 5, 9, . . . is the sequence of digits in the decimal expansion of π. (d) 3.9, 5.3, 7.2, 9.6, 12.9, 17.1, 23.1, 38.6, 50.2 is the sequence of U.S. population figures, in millions,for the census reports (1790 -1880). (e) 3.5, 4.2, 5.1, 5.9, 6.7, 8.1, 9.4, 10.6, 10.1, 7.1, 3.8, 2.1, 1.4, 1.1 is the sequence of pager subscribers in Japan, in millions, from the years 1989 -2002. Functions Modeling Change: A Preparation for Calculus, 4th
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Notation for Sequences and Examples Like Example 3 List the first 5 terms of the sequence a n = f ( n ), where f ( x ) = 400 − 20 x . Functions Modeling Change: A Preparation for Calculus, 4th
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Example 4 Which of the following sequences are arithmetic? (a) 9, 5, 1,−3,−7 (b) 3, 6, 12, 24, 48 (c) 2, 2 + p, 2 + 2p, 2 + 3p (d) 10, 5, 0, 5, 10 Solution (a) Each term is obtained from the previous term by subtracting 4. This sequence is arithmetic. (b) This sequence is not arithmetic: each terms is twice the previous term. The differences are 3, 6, 12, 24. (c) This sequence is arithmetic: p is added to each term to obtain the next term. (d) This is not arithmetic. The difference between the second and first terms is −5, but the difference between the fifth and fourth terms is 5. Functions Modeling
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ch.13 Sequences and Series - Chapter 13 Sequences and...

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