110quiz7solutions - Math 110 Quiz 7 Nov. 16, 2006 Solutions...

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Unformatted text preview: Math 110 Quiz 7 Nov. 16, 2006 Solutions 1 2 1 an-1 2 1) (a) List the first four terms of the sequence with nth term given by an = (-1)n+1 (4n + 1). (b) List the first four terms of the sequence with a1 = for n = 2, 3, 4, . . . Solutions: (a) 5, -9, 13, -17 (b) 1 1 , 4, , 256 2 16 and nth term given recursively by an = 2) For the following sequences, find the most evident expression for the nth term an . (a) 3, 7, 11, 15, . . . 1 (b) 2 , - 8 , 27 , - 64 , . . . 3 4 5 Solutions: (a) an = 4n - 1 (b) (-1)n+1 n3 n+1 1 3. What does the sequence given by an = 3n n+2 approach as n ? Solution: As n , this sequence gets closer and closer to 3 Another way to see this is that the function f (x) = has a horizontal asymptote at y = 3. 3x x+2 4. A company depreciates the value of its machinery according to the sequence an = 12000(1 - 0.04)n where an is the value of the machinery after n years. (a) Determine the first three terms of this sequence. (b) As n , what does the value of the machine approach? Solutions: (a) 11520, 11059.2, 10616.83 (b) Substituting larger and larger values of n, we see that the value of the machinery approaches 0 This is what one may expect. 2 ...
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This note was uploaded on 06/16/2008 for the course MATH 110 taught by Professor Carlson during the Spring '07 term at University of Arizona- Tucson.

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110quiz7solutions - Math 110 Quiz 7 Nov. 16, 2006 Solutions...

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