PP 12.1 - Sequences Definition A sequence can be thought of...

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Sequences
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Definition A sequence can be thought of as a list of numbers written in a definite order: a 1 , a 2 , a 3 , a 4 , …, a n , … The number a 1 is called the first term . a n is the n th term . We will deal exclusively with infinite sequences.
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Notice that, for every positive integer n , there is a corresponding number a n . Notation Hence a sequence can be defined as a function whose domain is the set of positive integers. f(n) = a n { a 1 , a 2 , a 3 , . . .} { } { } 1 or n n n a a =
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Notation Preceding Notation Defining Formula Terms of Sequence 1 1 n n n = + 1 n n a n = + 1 2 3 4 , , , ,. .., ,... 2 3 4 5 1 n n + A sequence can be described in several forms.
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Example Assuming the pattern of the first few terms continues, find a formula for the general term a n of the sequence 3 4 5 6 7 , , , , ,... 5 25 125 625 3125 - -
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We have: 1 2 3 4 5 3 4 5 5 25 125 6 7 625 3125 a a a a a = = - = = - = Are there any patterns? The terms alternate sign. The numerators increase by one, starting with 3. The denominators are powers of 5.
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n Numerator Denominator Sign 1 3 5 + 2 4 25 - 3 5 125 + 4 6 625 - n 5 1 ) 1 ( + - n Getting the Formula n n + 2 n n n n a 5 2 ) 1 ( 1 + - = +
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This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

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PP 12.1 - Sequences Definition A sequence can be thought of...

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