|
Author |
Message |
|
TAGS:
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9559
[2] , given: 826
|
The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
 14 Jun 2012, 02:38
2
This post received
KUDOS
Question Stats:
77% (02:20) correct
22% (01:01) wrong based on 6 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectThe 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 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Explanations (OE) to them along with an alternate approaches if necessary. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button (the best solution we'll be put along the OE in the second post); 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! _________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9559
[1] , given: 826
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
14 Jun 2012, 02:39
1
This post received
KUDOS
|
|
|
|
|
|
Manager
Joined: 29 Mar 2012
Posts: 246
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 10
Kudos [?]:
50
[1] , given: 20
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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}}2or 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_6Subtracting these equations; \frac{a_5-a_3}2=a_6-a_5a_6=\frac{3a_5-a_3}2=\frac{3*20-4}2=28Thus, Answer is (E). Regards,
_________________
My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules
My story: 640 What a blunder!
My page: Ed Prep
|
|
|
|
|
|
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]
14 Jun 2012, 06:11
a4=2*a6-a5;=>a4=40-4=36; therefore,a6=(36+20)/2=28;
IF U GUYS LIKE THE POST PLZ GIVE A KUDOS!!!! 
|
|
|
|
|
|
Intern
Joined: 03 Jun 2012
Posts: 32
Location: United States
WE: Project Management (Computer Software)
Followers: 0
Kudos [?]:
11
[0], given: 2
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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
Joined: 28 Jul 2011
Posts: 596
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1
Kudos [?]:
25
[0], given: 16
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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
Joined: 12 Apr 2011
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 2
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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
Joined: 13 Jan 2012
Posts: 271
Weight: 170lbs
WE: Analyst (Other)
Followers: 4
Kudos [?]:
50
[0], given: 28
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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
Joined: 07 Sep 2011
Posts: 65
Location: United States
Concentration: Strategy, International Business
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 3
Kudos [?]:
19
[0], given: 3
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9559
[0], given: 826
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
22 Jun 2012, 02:38
|
|
|
|
|
|
Senior Manager
Joined: 13 Aug 2012
Posts: 468
Followers: 12
Kudos [?]:
75
[0], given: 11
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
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
|
|
|
|
|
|
|
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1
[#permalink]
19 Dec 2012, 22:38
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
The sequence a1, a2, , a n, is such that an = 2an-1 - x for
|
Guest |
2 |
20 Oct 2004, 08:58 |
|
|
|
|
The sequence a1, a2, , a n, is such that an = 2an-1 - x
|
WinIT |
2 |
12 Nov 2006, 09:48 |
|
|
|
|
A1,A2,A3....A15 In the above sequence An=An-1+K where
|
arjsingh1976 |
3 |
09 Dec 2006, 09:39 |
|
|
1
|
|
a1, a2, a3, ... , a15 In the sequence shown, an = an-1 + k,
|
marcodonzelli |
9 |
10 Mar 2008, 11:47 |
|
|
|
|
The sequence a1, a2, , a n, is such that an = 2an-1 - x
|
arorag |
3 |
27 Sep 2008, 12:52 |
|
|
|
|
|
|
close
