Find all School-related info fast with the new School-Specific MBA Forum

It is currently 16 Apr 2014, 02:25

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
Joined: 23 Mar 2008
Posts: 226
Followers: 1

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

GMAT Tests User
If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 [#permalink] New post 06 May 2008, 11:05
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
Current Student
User avatar
Joined: 14 Apr 2008
Posts: 453
Schools: F2010 - HBS (R1 - denied w/o interview ), INSEAD (R1 - admitted), Wharton (R1 - waitlisted & ding), Ivey (R2 - admitted w/ 60% tuition)
WE 1: 3.5yrs as a Strategy Consultant - Big 4
Followers: 11

Kudos [?]: 33 [0], given: 16

GMAT Tests User
Re: sequence [#permalink] New post 06 May 2008, 11:27
hmm it took me a long time ... but lets try this ...

start writing out some of the resultants and should start seeing a pattern where each value corresponds to 2^xn + 1 ... therefore :

x20-x19 corresponds to (2^20 + 1) - (2^19 + 1) = 2^20- 2^19 = 2^19 (2-1) = 2^19

therefore the answer is A


OA?

puma 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

_________________

INSEAD Sept 2010 Interview Invite Nov 5, 2009 Admit & Matriculating
Wharton Sept 2010 Interview Invite Oct 30, 2009 Waitlisted & Ding
Harvard Sept 2010 Ding without Interview
Ivey May 2010 Interview Invite Nov 23, 2009 Admit + $$

Senior Manager
Senior Manager
Joined: 20 Feb 2008
Posts: 296
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
Followers: 4

Kudos [?]: 20 [0], given: 0

GMAT Tests User
Re: sequence [#permalink] New post 06 May 2008, 11:28
My answer is A 2^19

Xn+1 = 2Xn -1 ,X1=3

X2 = 3*2 -1 = 5 (X2-X1 = 2) 2^1

X3 =5*2 -1 = 9 (X3-X2 =4 ) 2^2

X4 = 9*2 -1 =17 (X4-X3 = 8 ) 2^3


So we have a pattern where Xn - Xn-1 =2^n-1

Therefore for X20 -X19 = 2^19
Current Student
Joined: 28 Dec 2004
Posts: 3411
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 148 [0], given: 2

GMAT Tests User
Re: sequence [#permalink] New post 06 May 2008, 11:37
puma 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


your post is not very clear..however..here is how i do it..

xn+1=(2xn)-1

x1=3, x2=5, x3=9 x4=17 x5=33

notice the difference btw x^5-x^4=2^4 or 16, x^4-x^3=2^3...

therefore x^20-x^19=2^19

A it is..
VP
VP
Joined: 10 Jun 2007
Posts: 1469
Followers: 5

Kudos [?]: 85 [0], given: 0

GMAT Tests User
Re: sequence [#permalink] New post 06 May 2008, 12:02
puma 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


X1 = 3 = 2^1 + 1
X2 = 5 = 2^2 + 1
X3 = 9 = 2^3 + 1

This means
x19 = 2^19 + 1
X20 = 2^20 + 1
X20 - X19 = 2^20 + 1 - 2^19 - 1 = 2^20 - 2^19 = 2^19*(2-1) = 2^19
Director
Director
Joined: 05 Jan 2008
Posts: 709
Followers: 2

Kudos [?]: 74 [0], given: 0

GMAT Tests User
Re: sequence [#permalink] New post 07 May 2008, 04:37
I got A

X2=2X1 -1=5=2^2+1

x3=2x2-1=10-1=2^3+1
...

x20-x19= 2x19-1-x19=x19-1

but x19=2^19+1

thus x19-1= 2^19+1-1=2^19
_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

Re: sequence   [#permalink] 07 May 2008, 04:37
    Similar topics Author Replies Last post
Similar
Topics:
New posts if x1, x2, x3......xn is such that x1 = 3 and xn+1 = 2.xn-1 damit 9 06 Sep 2004, 16:32
New posts If the sequence x1, x2, x3,..., xn,... is such that x1=3 and qhoc0010 7 18 Feb 2005, 08:54
New posts 1 If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more arjtryarjtry 5 30 Jul 2008, 17:32
New posts If the sequence X1, X2, X3, , Xn, is such thatX1 = 3 andXn+1 haichao 3 12 Nov 2008, 07:39
New posts The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) aeros232 2 22 Sep 2012, 09:19
Display posts from previous: Sort by

If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.