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

It is currently 29 Sep 2016, 08:35
GMAT Club Tests

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34899
Followers: 6498

Kudos [?]: 83030 [4] , given: 10134

The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 02:38
4
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

77% (02:19) correct 23% (01:09) wrong based on 861 sessions

HideShow timer Statistics

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

Diagnostic Test
Question: 3
Page: 20
Difficulty: 600
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34899
Followers: 6498

Kudos [?]: 83030 [2] , given: 10134

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 02:39
2
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 the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Kellogg MMM ThreadMaster
User avatar
Joined: 29 Mar 2012
Posts: 298
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 27

Kudos [?]: 362 [1] , given: 23

GMAT ToolKit User
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 05:58
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,
2 KUDOS received
Intern
Intern
avatar
Joined: 15 Dec 2011
Posts: 2
Followers: 0

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

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 06:11
2
This post received
KUDOS
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 [?]: 36 [0], given: 2

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 20:27
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
avatar
Joined: 28 Jul 2011
Posts: 563
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 2

Kudos [?]: 188 [0], given: 16

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 21:00
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
avatar
Joined: 12 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]

Show Tags

New post 14 Jun 2012, 23:36
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: 309
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE: Analyst (Other)
Followers: 15

Kudos [?]: 130 [0], given: 38

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jun 2012, 23:47
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: 6

Kudos [?]: 37 [0], given: 3

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 16 Jun 2012, 03:45
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
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34899
Followers: 6498

Kudos [?]: 83030 [0], given: 10134

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 22 Jun 2012, 02:38
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 the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 394 [0], given: 11

GMAT ToolKit User
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 19 Dec 2012, 22:38
\(a_3 = 4\)
\(a_4 = ?\)
\(a_5 = 20\)
\(a_6 = ?\)

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

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

Answer: (E) 28
_________________

Impossible is nothing to God.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11740
Followers: 529

Kudos [?]: 149 [0], given: 0

Premium Member
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jul 2014, 20:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 27 Aug 2014
Posts: 9
Followers: 0

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

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 27 Aug 2014, 17:26
Bunuel wrote:
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

Diagnostic Test
Question: 3
Page: 20
Difficulty: 600


Nice but easy problem. I think the idea is based on Fibonacci sequence.
Senior Manager
Senior Manager
User avatar
Joined: 10 Jul 2015
Posts: 276
GMAT 1: 770 Q47 V48
WE: Education (Education)
Followers: 24

Kudos [?]: 178 [0], given: 38

The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 14 Jul 2016, 19:47
Bunuel wrote:
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



Please note: this question in the 2017 version of the OG (page 20, #3, Quant Diagnostic Test) contains a typo. It should say \(a_n=\frac{a_{n-1}+a_{n-2}}{2}\) for all \(n\geq{3}\), but instead it says \(a_n=\frac{a_{n+1}+a_{n-2}}{2}\) for all \(n\geq{3}\). The answer explanation on page 46, however, lists the correct formula.

Yes, even the GMAC makes mistakes!
VP
VP
User avatar
Joined: 12 Aug 2015
Posts: 1003
Followers: 18

Kudos [?]: 149 [0], given: 271

GMAT ToolKit User CAT Tests
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

Show Tags

New post 26 Aug 2016, 04:16
Here A5=A4+A3/2 => A4=36
A6=36+20/2 => 18+10 => 28
SMASH that E
_________________

Give me a hell yeah ...!!!!!

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1   [#permalink] 26 Aug 2016, 04:16
    Similar topics Author Replies Last post
Similar
Topics:
17 Experts publish their posts in the topic A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 Bunuel 5 15 Jun 2016, 01:46
26 Experts publish their posts in the topic In a certain sequence of numbers, a1, a2, a3, ..., an, the nave 12 06 Oct 2013, 10:30
13 Experts publish their posts in the topic The sequence of numbers a1, a2, a3, ..., an is defined by an farukqmul 5 09 Jun 2013, 05:31
7 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 11 18 Nov 2009, 13:48
5 Experts publish their posts in the topic The sequence a1, a2, … , a n, … is such that an = 2an-1 - x jet1445 11 04 Jun 2007, 20:23
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.