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# Sequence Problem

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Intern
Joined: 27 Aug 2012
Posts: 18

Kudos [?]: 7 [0], given: 55

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01 Dec 2012, 01:32
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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

Kudos [?]: 7 [0], given: 55

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 618

Kudos [?]: 793 [1], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)

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01 Dec 2012, 11:12
1
KUDOS
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

Hope it helps!
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Ankit

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Kudos [?]: 793 [1], given: 59

Intern
Joined: 27 Aug 2012
Posts: 18

Kudos [?]: 7 [0], given: 55

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01 Dec 2012, 19:53
Fine thanks. I idenitified the terms in the sequence, but failed to identify the sequence or pattern.

Kudos [?]: 7 [0], given: 55

Re: Sequence Problem   [#permalink] 01 Dec 2012, 19:53
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# Sequence Problem

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