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Progression

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Progression

by simplythebest » Wed Jun 06, 2007 2:28 am
The sequence a1, a2, … , a n, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x?
A. 3
B. 9
C. 18
D. 36
E. 45
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Re: Progression

by jayhawk2001 » Wed Jun 06, 2007 6:15 am
simplythebest wrote:The sequence a1, a2, … , a n, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x?
A. 3
B. 9
C. 18
D. 36
E. 45
a5 = 2a4 - x = 2 (2a3 - x) - x = 4a3 - 3x
So, 3x = 4a3 - a5 = 4*27 - 99 = 3*(36-33) = 3*3

x = 3
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