It is currently 11 Dec 2017, 02:47

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42536

Kudos [?]: 135189 [2], given: 12671

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

### Show Tags

14 Jun 2012, 02:38
2
KUDOS
Expert's post
13
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

78% (01:23) correct 22% (01:15) wrong based on 1446 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

_________________

Kudos [?]: 135189 [2], given: 12671

Math Expert
Joined: 02 Sep 2009
Posts: 42536

Kudos [?]: 135189 [4], given: 12671

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

### Show Tags

14 Jun 2012, 02:39
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
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:

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

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

_________________

Kudos [?]: 135189 [4], given: 12671

Joined: 29 Mar 2012
Posts: 320

Kudos [?]: 536 [1], given: 23

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 = an-1 [#permalink]

### Show Tags

14 Jun 2012, 05:58
1
KUDOS
1
This post was
BOOKMARKED
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;
$$\frac{a_5-a_3}2=a_6-a_5$$
$$a_6=\frac{3a_5-a_3}2=\frac{3*20-4}2=28$$

Regards,

Kudos [?]: 536 [1], given: 23

Intern
Joined: 15 Dec 2011
Posts: 2

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

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

### Show Tags

14 Jun 2012, 06:11
3
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!!!!

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

Intern
Joined: 03 Jun 2012
Posts: 30

Kudos [?]: 53 [0], given: 2

Location: United States
WE: Project Management (Computer Software)
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#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.

Kudos [?]: 53 [0], given: 2

Director
Joined: 28 Jul 2011
Posts: 516

Kudos [?]: 311 [0], given: 16

Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#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
_________________

Kudos [?]: 311 [0], given: 16

Intern
Joined: 12 Apr 2011
Posts: 2

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

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

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

Senior Manager
Joined: 13 Jan 2012
Posts: 304

Kudos [?]: 229 [0], given: 38

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 = an-1 [#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

Kudos [?]: 229 [0], given: 38

Manager
Joined: 07 Sep 2011
Posts: 63

Kudos [?]: 40 [0], given: 3

Location: United States
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#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 40-4=a4.

a6= 20+36/2= 28

Kudos [?]: 40 [0], given: 3

Senior Manager
Joined: 13 Aug 2012
Posts: 457

Kudos [?]: 568 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

### Show Tags

19 Dec 2012, 22:38
$$a_3 = 4$$
$$a_4 = ?$$
$$a_5 = 20$$
$$a_6 = ?$$

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

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

_________________

Impossible is nothing to God.

Kudos [?]: 568 [0], given: 11

Intern
Joined: 27 Aug 2014
Posts: 8

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

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

### Show Tags

27 Aug 2014, 17:26
Bunuel wrote:
The sequence $$a_1$$, $$a_2$$, $$a_3$$, ... , $$a_n$$, ... is such that $$a_n=\frac{a_{n-1}+a_{n-2}}{2}$$ 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.

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

Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 438

Kudos [?]: 515 [0], given: 58

Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)
The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

### Show Tags

14 Jul 2016, 19:47
Bunuel wrote:
The sequence $$a_1$$, $$a_2$$, $$a_3$$, ... , $$a_n$$, ... is such that $$a_n=\frac{a_{n-1}+a_{n-2}}{2}$$ 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!
_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and online via Skype, since 2002.

GMAT Action Plan - McElroy Tutoring

Kudos [?]: 515 [0], given: 58

Retired Moderator
Joined: 12 Aug 2015
Posts: 2209

Kudos [?]: 898 [0], given: 607

GRE 1: 323 Q169 V154
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

### Show Tags

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 ...!!!!!

Kudos [?]: 898 [0], given: 607

Senior Manager
Joined: 25 Mar 2013
Posts: 274

Kudos [?]: 35 [0], given: 101

Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#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

Kudos [?]: 35 [0], given: 101

Manager
Joined: 18 Oct 2016
Posts: 139

Kudos [?]: 60 [0], given: 90

Location: India
WE: Engineering (Energy and Utilities)
Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]

### Show Tags

18 Apr 2017, 22:27
Option E

$$a_n=\frac{a_{n-1}+a_{n-2}}{2}$$

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!

Kudos [?]: 60 [0], given: 90

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1   [#permalink] 18 Apr 2017, 22:27
Display posts from previous: Sort by