Last visit was: 19 Nov 2025, 21:28 It is currently 19 Nov 2025, 21:28
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
705-805 Level|   Sequences|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,392
 [5]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,392
 [5]
A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 01 Nov 2023, 00:59
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

59% (02:33) correct 41% (02:58) wrong based on 126 sessions

History

Date
Time
Result
Not Attempted Yet
A sequence is defined by \(a_{n} = a_{n-1} − a_{n-2}\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5
ShowHide Answer
Official Answer
B
User avatar
varad98
User avatar
Joined: 06 Aug 2022
Last visit: 02 Mar 2025
Posts: 60
Own Kudos:
26
 [2]
Given Kudos: 35
GMAT Focus 1: 645 Q86 V81 DI79
GMAT 1: 690 Q50 V34
GPA: 3.8
Products:
My Reviews
GMAT Focus 1: 645 Q86 V81 DI79
GMAT 1: 690 Q50 V34
Posts: 60
Kudos: 26
 [2]
A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 03 Nov 2023, 01:25
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5
Show more

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.
User avatar
RiyazAhamed
User avatar
Joined: 27 May 2022
Last visit: 17 Feb 2024
Posts: 16
Own Kudos:
22
 [1]
Given Kudos: 369
GMAT 1: 400 Q32 V14
GMAT 2: 500 Q38 V21
GMAT 3: 550 Q41 V26
GMAT 3: 550 Q41 V26
Posts: 16
Kudos: 22
 [1]
A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 13 Nov 2023, 03:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
varad98
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.
Show more

How did you get the term 3? When we substitute 3 for n, we get a5 = a4 - a3. Is there a typo (instead of negative, I think it is given positive) in the given sequence?
User avatar
samarpan.g28
User avatar
Joined: 08 Dec 2023
Last visit: 19 Nov 2025
Posts: 324
Own Kudos:
125
 [1]
Given Kudos: 1,236
Location: India
Concentration: General Management, Human Resources
Schools: IIMA '26 Schulich Sept '26 Montreal '26 HEC Sept '26
GPA: 8.88
WE:Engineering (Technology)
Schools: IIMA '26 Schulich Sept '26 Montreal '26 HEC Sept '26
Posts: 324
Kudos: 125
 [1]
A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 21 Dec 2023, 23:58
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
varad98
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.
Show more

I understood the solution, however, if n>=3 is already mentioned, how can we take n=1 to find the value of a3? Please help.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,392
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,392
A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 22 Dec 2023, 00:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
samarpan.g28
varad98
Bunuel
A sequence is defined by \(a_{n+2} = a_{n+1} − a_n\) for \(n ≥ 3\). If \(a_1 = 3\) and \(a_2 = 5\), what is the value of \(a_{2014}\)?

(A) −5
(B) −3
(C) 2
(D) 3
(E) 5

Using provided formula. we get
a1=3
a2=5
a3=2
a4=-3
a5=-5
a6=-2
a7=3=a1

The sequence is made of 6 terms.
Hence divide 2014/6
Remainder= 4
Hence Selecting the 4th Term=-3

Hope this is correct.

I understood the solution, however, if n>=3 is already mentioned, how can we take n=1 to find the value of a3? Please help.
Show more

Yes, it would have been better if it were \(a_{n} = a_{n-1} − a_{n-2}\) instead. Fixed. Thank you!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
A sequence is defined by an+2 = an+1 an for n 1. If a1 = 3 and a2 06 Jan 2025, 02:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts