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

It is currently 22 Oct 2014, 16:48

Starting Soon!

Live Q&A Session with HKU Admissions Team | Join the chat room to participate.


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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 19 Nov 2005
Posts: 17
Followers: 0

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

If the sequence x1, x2, x3, , xn, is such that x1 = 3 and [#permalink] New post 28 Nov 2005, 07:10
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n ≥ 1, then x20 – x19 =

A. 219
B. 220
C. 221
D. 220 - 1
E. 221 - 1
_________________

Tanmoi.

Director
Director
avatar
Joined: 14 Sep 2005
Posts: 996
Location: South Korea
Followers: 2

Kudos [?]: 34 [0], given: 0

 [#permalink] New post 28 Nov 2005, 16:21
X(n+1) = 2X(n) - 1

X(1) = P
X(2) = 2P - 1
X(3) = 2(2P - 1) - 1 = 4P - 2 - 1
X(4) = 2(4P - 2 - 1 ) - 1 = 8P - 4 - 2 - 1
X(5) = 2(8P - 4 - 2 - 1) - 1 = 16P - 8 - 4 - 2 - 1

Thus, X(n) = 2^(n-1)P - 2^(n-1) + 1

X(19) = 2^18 * P - 2^18 + 1
= 2^18(P - 1) + 1
= 2^19 + 1
_________________

Auge um Auge, Zahn um Zahn :twisted: !

SVP
SVP
User avatar
Joined: 24 Sep 2005
Posts: 1898
Followers: 10

Kudos [?]: 109 [0], given: 0

Re: Sequence PS [#permalink] New post 28 Nov 2005, 16:45
Tanmoi 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. 219
B. 220
C. 221
D. 220 - 1
E. 221 - 1


can you double-check the bold part?? ...xn+1 is xn + 1?? or the (n+1)th term???

the answer choices, are they 2^ 19, 2^20,...?
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5095
Location: Singapore
Followers: 19

Kudos [?]: 155 [0], given: 0

 [#permalink] New post 28 Nov 2005, 17:28
The answer choices....

A = 219, but D is also 219 (220-1), B is 220, but E is also 220 (221-1)

Something wrong?? Or there's some subscript that we're not aware of
Senior Manager
Senior Manager
User avatar
Joined: 14 Apr 2005
Posts: 422
Location: India, Chennai
Followers: 1

Kudos [?]: 3 [0], given: 0

Re: Sequence PS [#permalink] New post 29 Nov 2005, 03:56
Tanmoi 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. 219
B. 220
C. 221
D. 220 - 1
E. 221 - 1

I think the answer choices should be 2 to the powers. Here is my working.
X1 =3,
X2=5
X3=9
X4-17, we are having a pattern here. It is Xn = (2^n)-1
So X20 = (2^20)-1
X19 = (2^19) -1
X20 -X19 = (2^20-1)-(2^19-1)
= 2^20 - 2^19
= 2^19(2-1)
= 2^19
A.
Intern
Intern
avatar
Joined: 22 Mar 2005
Posts: 39
Location: Houston
Followers: 0

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

 [#permalink] New post 29 Nov 2005, 06:48
I get 2^19 as well as the difference between two consecutive terms can be expressed as 2 raised to power of the lower term.

x1 = 3
x2 = 5 (x2-x1 = 2 or 2^1)
x3 = 9 (x3-x2 = 4 or 2^2)
x4 = 17 (x4-x3 = 8 or 2^3)

So x12-x11 = 2^11
And x20-x19 = 2^19

Furthermore, the difference between non-consecutive terms can be expressed by summing the differences of the consecutive terms in between them, that would have been an interesting question.

For example, x5 - x2 = 2^2+2^3+2^4 = 28 which is indeed 33-5.
Senior Manager
Senior Manager
avatar
Joined: 03 Nov 2005
Posts: 399
Location: Chicago, IL
Followers: 3

Kudos [?]: 25 [0], given: 17

 [#permalink] New post 29 Nov 2005, 20:36
could somebody post A detailed explanation, please?
_________________

Hard work is the main determinant of success

  [#permalink] 29 Nov 2005, 20:36
    Similar topics Author Replies Last post
Similar
Topics:
If the sequence X1, X2, X3, , Xn, is such thatX1 = 3 andXn+1 haichao 3 12 Nov 2008, 07:39
1 If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is jimmylow 3 17 Jul 2008, 02:03
If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 puma 5 06 May 2008, 11:05
If the sequence x1, x2, x3, , xn, is such that x1 = 3 and sperumba 6 16 Jan 2006, 08:57
If the sequence x1, x2, x3, , xn, is such that x1 = 3 and desiguy 1 08 Dec 2005, 16:14
Display posts from previous: Sort by

If the sequence x1, x2, x3, , xn, is such that x1 = 3 and

  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®.