Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50007

The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
14 Jun 2012, 02:38
Question Stats:
84% (01:49) correct 16% (01:48) wrong based on 1660 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 50007

The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
14 Jun 2012, 02:39
SOLUTIONThe sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n1}+a_{n2}}{2}\) 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 \(a_n=\frac{a_{n1}+a_{n2}}{2}\), then: \(a_5=\frac{a_{4}+a_{3}}{2}\) > \(20=\frac{a_{4}+4}{2}\) > \(a_4=36\); \(a_6=\frac{a_{5}+a_{4}}{2}\) > \(a_6=\frac{20+36}{2}\) > \(a_6=28\). Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics




Current Student
Joined: 29 Mar 2012
Posts: 316
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
14 Jun 2012, 05:58
Hi,
This one has be solved step by step, and there is chance of making mistakes.
Difficulty level: 600
\(a_n=\frac{a_{n1}+a_{n2}}2\) 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; \(\frac{a_5a_3}2=a_6a_5\) \(a_6=\frac{3a_5a_3}2=\frac{3*204}2=28\)
Thus, Answer is (E).
Regards,



Intern
Joined: 15 Dec 2011
Posts: 2

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
14 Jun 2012, 06:11
a4=2*a6a5;=>a4=404=36; therefore,a6=(36+20)/2=28;
IF U GUYS LIKE THE POST PLZ GIVE A KUDOS!!!!



Intern
Joined: 03 Jun 2012
Posts: 29
Location: United States
WE: Project Management (Computer Software)

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
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.



Senior Manager
Joined: 28 Jul 2011
Posts: 370
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
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

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
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: 286
Weight: 170lbs
GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42
WE: Analyst (Other)

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
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: 61
Location: United States
Concentration: Strategy, International Business
WE: General Management (Real Estate)

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
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 404=a4.
a6= 20+36/2= 28
Answer: E



Senior Manager
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
19 Dec 2012, 22:38
\(a_3 = 4\) \(a_4 = ?\) \(a_5 = 20\) \(a_6 = ?\) \(a_n=\frac{a_{n1} + a_{n2}}{2}\) \(20(2)=\frac{4 + a_4}{2}\) \(40=4 + a_4\) \(36 = a_4\) \(a_6 = \frac{20 + 36}{2}=28\) Answer: (E) 28
_________________
Impossible is nothing to God.



Intern
Joined: 27 Aug 2014
Posts: 6

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
27 Aug 2014, 17:26
Bunuel wrote: The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n1}+a_{n2}}{2}\) 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.



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 671
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
14 Jul 2016, 19:47
Bunuel wrote: The sequence \(a_1\), \(a_2\), \(a_3\), ... , \(a_n\), ... is such that \(a_n=\frac{a_{n1}+a_{n2}}{2}\) 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 \(a_n=\frac{a_{n1}+a_{n2}}{2}\) for all \(n\geq{3}\), but instead it says \(a_n=\frac{a_{n+1}+a_{n2}}{2}\) for all \(n\geq{3}\). The answer explanation on page 46, however, lists the correct formula. Yes, even the GMAC makes mistakes!
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.)
...or find me on Reddit: http://www.reddit.com/r/GMATpreparation



Current Student
Joined: 12 Aug 2015
Posts: 2638

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
26 Aug 2016, 04:16



Manager
Joined: 25 Mar 2013
Posts: 247
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
13 Jan 2017, 14:33
a3 =4, a5 = 20 a5 = \(\frac{a4 + a3}{2}\) 20 =\(\frac{a4 + 4}{2}\) 40  4 = a4 a4 = 36 a6 = \(\frac{20 + 36}{2}\) 28 E
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you



Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
18 Apr 2017, 22:27
Option E\(a_n=\frac{a_{n1}+a_{n2}}{2}\) a\(_5 = 20, a_3 = 4\) \(a_5=\frac{a_{4}+a_{3}}{2}\) \(a_4 = 36\) \(a_6=\frac{a_{5}+a_{4}}{2}\) = 28
_________________
Press Kudos if you liked the post!
Rules for posting  PLEASE READ BEFORE YOU POST



Manager
Joined: 13 Feb 2018
Posts: 135

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
29 May 2018, 01:21
Bunuel wrote: SOLUTION
\(a_6=\frac{a_{5}+a_{4}}{2}\) > \(a_6=\frac{20+36}{2}\) > \(a_5=28\).
Answer: E. Dear Bunuel seems there is a typo Instead of \(a_5=28\) there must be \(a_6=28\) or I didn't get somthing



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1
[#permalink]
Show Tags
29 May 2018, 07:43




Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an1 &nbs
[#permalink]
29 May 2018, 07:43






