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Sequence Problem

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Intern
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Joined: 27 Aug 2012
Posts: 21
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Sequence Problem [#permalink] New post 01 Dec 2012, 00:32
If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n ≥ 1, then x20 – x19 =

A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1

[Reveal] Spoiler:
A


I get x19 = 38. But I am not able to match to 2^19. I doubt if the definition of xn+1 is wrong. Can anyone comment? Source : GMAT MATH SET 1
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Status: If you think you can, then eventually you WILL!
Joined: 05 Apr 2011
Posts: 400
Location: India
Concentration: Finance, Marketing
Schools: ISB '14 (D)
GMAT 1: 570 Q49 V19
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WE: Information Technology (Computer Software)
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Kudos [?]: 192 [1] , given: 39

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Re: Sequence Problem [#permalink] New post 01 Dec 2012, 10:12
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SreeViji wrote:
If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n ≥ 1, then x20 – x19 =

A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1

[Reveal] Spoiler:
A


I get x19 = 38. But I am not able to match to 2^19. I doubt if the definition of xn+1 is wrong. Can anyone comment? Source : GMAT MATH SET 1



terms in the sequence are 3,5,9,17,...
xn = 2^n + 1
so, x^20 - x^19 = (2^20 +1)- (2^19 +1)
= 2^20 - 2^19
= 2*2^19 - 2^19
= 2^19

Answer will be A
Hope it helps!
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Intern
Intern
Joined: 27 Aug 2012
Posts: 21
Followers: 0

Kudos [?]: 1 [0], given: 55

Re: Sequence Problem [#permalink] New post 01 Dec 2012, 18:53
Fine thanks. I idenitified the terms in the sequence, but failed to identify the sequence or pattern.
Re: Sequence Problem   [#permalink] 01 Dec 2012, 18:53
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