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If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is

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If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is [#permalink] New post 17 Jul 2008, 02:03
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If the sequence \(x{_1}\), \(x{_2}\), \(x{_3}\), ...., \(x{_n}\), ....is such that \(x{_1}\) = 3 and \(x{_n_+_1}\) = \(2x{_n} - 1\) for n >= 1, then \(x{_2_0}\) - \(x{_1_9}\) =

A. \(2^{19}\)
B. \(2^{20}\)
C. \(2^{21}\)
D. \(2^{20} -1\)
E. \(2^{21} -1\)
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Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
GMAT Malaysia: http://gmatmalaysia.blogspot.com

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Re: Math Set 1: Q25 [#permalink] New post 17 Jul 2008, 02:51
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jimmylow wrote:
If the sequence \(x{_1}\), \(x{_2}\), \(x{_3}\), ...., \(x{_n}\), ....is such that \(x{_1}\) = 3 and \(x{_n_+_1}\) = \(2x{_n} - 1\) for n >= 1, then \(x{_2_0}\) - \(x{_1_9}\) =

A. \(2^{19}\)
B. \(2^{20}\)
C. \(2^{21}\)
D. \(2^{20} -1\)
E. \(2^{21} -1\)


A

if you do out the first few, you'll see a pattern.

x1 = 3
x2 = 2*3-1 = 5
x3 = 2*5-1 = 9
x4 = 2*9-1 = 17

x2-x1 = 2
x3-x2 = 4 = 2^2
x4-x3 = 2^3
.
.
.
x20-x19 = 2^19
Manager
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Re: Math Set 1: Q25 [#permalink] New post 17 Jul 2008, 03:00
Thks mate. 1 kudos for you
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Jimmy Low, Frankfurt, Germany
Blog: http://mytrainmaster.wordpress.com
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Re: Math Set 1: Q25 [#permalink] New post 17 Jul 2008, 03:46
jimmylow wrote:
If the sequence \(x{_1}\), \(x{_2}\), \(x{_3}\), ...., \(x{_n}\), ....is such that \(x{_1}\) = 3 and \(x{_n_+_1}\) = \(2x{_n} - 1\) for n >= 1, then \(x{_2_0}\) - \(x{_1_9}\) =

A. \(2^{19}\)
B. \(2^{20}\)
C. \(2^{21}\)
D. \(2^{20} -1\)
E. \(2^{21} -1\)



every term in sequence is 2^n + 1....where n >=1

x20 = 2^20 + 1
x19 = 2^19 + 1

subtracting x19 from x20

2*2^19 + 1 - 2^19 -1

2^19(2-1)

2^19

A.
Re: Math Set 1: Q25   [#permalink] 17 Jul 2008, 03:46
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If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is

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