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

It is currently 28 Aug 2014, 03:50

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 17 Aug 2005
Posts: 394
Location: Boston, MA
Followers: 1

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

GMAT Tests User
If the sequence x1, x2, x3, ... xn, ... is such that x1 = 3 [#permalink] New post 25 Mar 2006, 13:50
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

80% (02:25) correct 20% (03:54) wrong based on 10 sessions
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\geq1, then x_{20} - x_{19} equals which of the following?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-sequence-x1-x2-x3-xn-is-such-that-x1-98536.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 May 2014, 05:50, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
Manager
Manager
avatar
Joined: 20 Nov 2004
Posts: 109
Followers: 0

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

GMAT Tests User
Re: PS-sequence [#permalink] New post 25 Mar 2006, 15:22
Well the answer seems to be 2^19 and A (although your A states 219).
Just write down the first elements and compute the differences.

x1=3
x2=5
x3=9
x4=17

So
x2=x1+2^1
x3=x2+2^2
x4=x3+2^3
... and
x20=x19+2^19, so

x20-x19=2^19.
Intern
Intern
avatar
Joined: 30 Mar 2013
Posts: 29
Followers: 0

Kudos [?]: 8 [0], given: 29

Re: PS-sequence [#permalink] New post 24 May 2014, 05:33
ccax wrote:
Well the answer seems to be 2^19 and A (although your A states 219).
Just write down the first elements and compute the differences.

x1=3
x2=5
x3=9
x4=17

So
x2=x1+2^1
x3=x2+2^2
x4=x3+2^3
... and
x20=x19+2^19, so

x20-x19=2^19.



sorry how did you get x2 =5 and so on? I'm not even understanding the question....x (n+1)=2x(n)-1......isnt this the questions? then how does everything goes into powers of two? Please help!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22143
Followers: 3407

Kudos [?]: 24906 [0], given: 2697

Re: PS-sequence [#permalink] New post 24 May 2014, 05:52
Expert's post
usre123 wrote:
ccax wrote:
Well the answer seems to be 2^19 and A (although your A states 219).
Just write down the first elements and compute the differences.

x1=3
x2=5
x3=9
x4=17

So
x2=x1+2^1
x3=x2+2^2
x4=x3+2^3
... and
x20=x19+2^19, so

x20-x19=2^19.



sorry how did you get x2 =5 and so on? I'm not even understanding the question....x (n+1)=2x(n)-1......isnt this the questions? then how does everything goes into powers of two? Please help!


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\geq1, then x_{20} - x_{19} equals which of the following?

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

We have the sequence x_1, x_2, x_3, …, x_n,x_1=3 and x_{n+1}=2x_n - 1 for n\geq1.

If you notice there is a specific pattern in it:

x_1=3=2^1+1
x_2=2x_1-1=5=2^2+1
x_3=2x_2-1=9=2^3+1
...
x_n=2^n+1

So, x_{20}=2^{20}+1 and x_{19}=2^{19}+1.

x_{20}-x_{19}=2^{20}+1-2^{19}-1=2^{20}-2^{19}=2^{19}

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-sequence-x1-x2-x3-xn-is-such-that-x1-98536.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: PS-sequence   [#permalink] 24 May 2014, 05:52
    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 qhoc0010 7 18 Feb 2005, 08:54
Display posts from previous: Sort by

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

  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®.