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

It is currently 19 Apr 2014, 21:51

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

The sequence a1, a2, a3, ... ,an, ... is such that an = an-1

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17321
Followers: 2875

Kudos [?]: 18404 [2] , given: 2350

GMAT Tests User CAT Tests
The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 01:38
2
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (02:18) correct 24% (00:57) wrong based on 239 sessions
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17321
Followers: 2875

Kudos [?]: 18404 [1] , given: 2350

GMAT Tests User CAT Tests
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 01:39
1
This post received
KUDOS
Expert's post
SOLUTION

The sequence a_1, a_2, a_3, ... , a_n, ... is such that a_n=\frac{a_{n-1}+a_{n-2}}{2} for all n\geq{3}. If a_3 = 4 and a_5 = 20, what is the value of a_6 ?

(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

Since given that a_n=\frac{a_{n-1}+a_{n-2}}{2}, then:

a_5=\frac{a_{4}+a_{3}}{2} --> 20=\frac{a_{4}+4}{2} --> a_4=36;

a_6=\frac{a_{5}+a_{4}}{2} --> a_6=\frac{20+36}{2} --> a_5=28.

Answer: E.
_________________

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

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 28 Mar 2012
Posts: 280
Concentration: Entrepreneurship, Sustainability
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 13

Kudos [?]: 111 [1] , given: 23

GMAT ToolKit User GMAT Tests User
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 04:58
1
This post received
KUDOS
Hi,

This one has be solved step by step, and there is chance of making mistakes.

Difficulty level: 600

a_n=\frac{a_{n-1}+a_{n-2}}2
or a_n is the average of last two terms,
thus,
\frac{a_3+a_4}2=a_5
\frac{a_4+a_5}2=a_6
Subtracting these equations;
\frac{a_5-a_3}2=a_6-a_5
a_6=\frac{3a_5-a_3}2=\frac{3*20-4}2=28

Thus, Answer is (E).

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Intern
Intern
Joined: 15 Dec 2011
Posts: 2
Followers: 0

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

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 05:11
a4=2*a6-a5;

=>a4=40-4=36; therefore,a6=(36+20)/2=28;

IF U GUYS LIKE THE POST PLZ GIVE A KUDOS!!!! 8-)
Intern
Intern
User avatar
Joined: 03 Jun 2012
Posts: 32
Location: United States
WE: Project Management (Computer Software)
Followers: 0

Kudos [?]: 15 [0], given: 2

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 19:27
a5 = (a3+a4) / 2
=> a4 = 2(a5) - a3
= 2 x 20 - 4 = 36

a6 = (a4+a5) / 2
= (36 + 20) / 2
= 28

Option E is correct.

Difficulty level is 600.
Director
Director
Joined: 28 Jul 2011
Posts: 588
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1

Kudos [?]: 30 [0], given: 16

GMAT Tests User
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 20:00
Its E

from the given formula we can deduce A4 and then take average of A4 and A5 and there is your answer
_________________

+1 Kudos If found helpful..

Intern
Intern
Joined: 11 Apr 2011
Posts: 2
Followers: 0

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

GMAT ToolKit User
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 22:36
its E.

a5=(a4+a3)/2
substituting you get a4=36

now a6=(a5+a4)/2
substitute to get a6 as 28
Senior Manager
Senior Manager
User avatar
Joined: 13 Jan 2012
Posts: 298
Weight: 170lbs
GMAT 1: 730 Q48 V42
GMAT 2: 740 Q48 V42
WE: Analyst (Other)
Followers: 7

Kudos [?]: 47 [0], given: 35

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 14 Jun 2012, 22:47
I'm not sure how efficient my method was:

a3 = 4 = (a2 + a1) / 2
:. 8 = a2 + a1

a5 = 20 = (a4 + a3) / 2
:. 40 = a4 + a3 = a4 + 4
:. a4 = 36

a6 = ?
a6 = (a5 + a4) / 2
a6 = (20 + 36) / 2 = 28

(E) 28
Manager
Manager
User avatar
Joined: 07 Sep 2011
Posts: 64
Location: United States
Concentration: Strategy, International Business
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 3

Kudos [?]: 24 [0], given: 3

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 16 Jun 2012, 02:45
I consider it to be higher then 600 level due to function involved although very each one if one is able to decipher.

Calculate the value of a4 as a5 and a3 is given. Thus a5=a4+a3/2
20=(a4+4)/2 or 40-4=a4.

a6= 20+36/2= 28

Answer: E
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17321
Followers: 2875

Kudos [?]: 18404 [0], given: 2350

GMAT Tests User CAT Tests
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 22 Jun 2012, 01:38
Expert's post
SOLUTION

The sequence a_1, a_2, a_3, ... , a_n, ... is such that a_n=\frac{a_{n-1}+a_{n-2}}{2} for all n\geq{3}. If a_3 = 4 and a_5 = 20, what is the value of a_6 ?

(A) 12
(B) 16
(C) 20
(D) 24
(E) 28

Since given that a_n=\frac{a_{n-1}+a_{n-2}}{2}, then:

a_5=\frac{a_{4}+a_{3}}{2} --> 20=\frac{a_{4}+4}{2} --> a_4=36;

a_6=\frac{a_{5}+a_{4}}{2} --> a_6=\frac{20+36}{2} --> a_5=28.

Answer: E.
_________________

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

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 465
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 14

Kudos [?]: 152 [0], given: 11

GMAT ToolKit User GMAT Tests User
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink] New post 19 Dec 2012, 21:38
a_3 = 4
a_4 = ?
a_5 = 20
a_6 = ?

a_n=\frac{a_{n-1} + a_{n-2}}{2}
20(2)=\frac{4 + a_4}{2}
40=4 + a_4
36 = a_4

a_6 = \frac{20 + 36}{2}=28

Answer: (E) 28
_________________

Impossible is nothing to God.

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1   [#permalink] 19 Dec 2012, 21:38
    Similar topics Author Replies Last post
Similar
Topics:
New posts The sequence a1, a2, , a n, is such that an = 2an-1 - x for Guest 2 20 Oct 2004, 07:58
New posts The sequence a1, a2, , a n, is such that an = 2an-1 - x WinIT 2 12 Nov 2006, 08:48
New posts A1,A2,A3....A15 In the above sequence An=An-1+K where arjsingh1976 3 09 Dec 2006, 08:39
Popular new posts 2 Experts publish their posts in the topic Consider a sequence a_1, a_2, a_3, a_4, ..., a_{n-2}, a_{n-1 BarneyStinson 10 18 Nov 2009, 12:48
New posts 1 Experts publish their posts in the topic For the sequence a1,a2,a3,…, an,an=an−1+an−2 for all values goodyear2013 1 28 Feb 2014, 09:49
Display posts from previous: Sort by

The sequence a1, a2, a3, ... ,an, ... is such that an = an-1

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.