Last visit was: 23 Apr 2026, 23:45 It is currently 23 Apr 2026, 23:45
Home
Messages
Tests
Schools
Events
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
655-705 (Hard)|   Sequences|      
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
 [25]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
 [25]
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 26 Jul 2017, 01:14
2
Kudos
Add Kudos
23
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

69% (02:43) correct 31% (02:48) wrong based on 256 sessions

History

Date
Time
Result
Not Attempted Yet
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+A2+A1. What is the ratio of A14 to A11?

A. 32
B. 16
C. 8
D. 4
E. 2
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,000
 [7]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,000
 [7]
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 28 Jul 2017, 01:26
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
==> If A11=A10+A9+A8+….+A2+A1=p, you get A12 =A11+A10+A11+….+A2+A1=2p, and from A13=4p, A14=8p, you get A14:A11=8p:p=8:1=8.

The answer is C.
Answer: C
General Discussion
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,800
Own Kudos:
6,235
 [2]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,800
Kudos: 6,235
 [2]
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 26 Jul 2017, 01:26
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We know that An+2=An+1+An+An-1+….+A2+A1
Given data: A1=1 and A2=2

From the above information, A3 = A1 + A2 = 1 + 2 = 3
Similarly, A4 = 3 + 2 + 1 = 6

The sequence will be 1,2,3,6,12,24,48,96,192,384,384*2,384*4,384*8,384*16.

The ratio of A14 to A11 is \(\frac{384*16}{384*2}\) = 8(Option C)
avatar
AbhimanyuDhar
avatar
Joined: 14 Oct 2016
Last visit: 07 May 2019
Posts: 29
Own Kudos:
37
Given Kudos: 155
Location: India
WE:Sales (Energy)
Posts: 29
Kudos: 37
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 08 Sep 2017, 11:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A(1)=1, A(2)=2, A(3)= 3, A(4)=6, A(5)=12
Seq after n>3 is [2^(n-3)] *3

Let us say x=3
so A(14)= [(2^13)*x]
and A(11)= [(2^8)*x]

ratio would be [(2^13)*x] / [(2^8)*x]
then it would be just [(2^11)]/[(2^8)]= 2^3
User avatar
rghvaggarwal
User avatar
Joined: 20 Jan 2017
Last visit: 07 Mar 2018
Posts: 4
Own Kudos:
2
Given Kudos: 12
Schools: Mannheim"19
Schools: Mannheim"19
Posts: 4
Kudos: 2
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 12 Sep 2017, 19:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can you please tell me how derived information for A3
avatar
AbhimanyuDhar
avatar
Joined: 14 Oct 2016
Last visit: 07 May 2019
Posts: 29
Own Kudos:
37
Given Kudos: 155
Location: India
WE:Sales (Energy)
Posts: 29
Kudos: 37
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 12 Sep 2017, 22:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rghvaggarwal
Can you please tell me how derived information for A3
Show more


We are given that each next term of the seq if formed by adding all the previous terms.

A3= A1+A2
avatar
OhMy
avatar
Joined: 11 Feb 2018
Last visit: 15 Nov 2022
Posts: 41
Own Kudos:
113
Given Kudos: 125
Status:resting for now
Location: Germany
Concentration: Technology, Strategy
Products:
My Reviews
Posts: 41
Kudos: 113
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 25 Dec 2019, 03:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AbhimanyuDhar
A(1)=1, A(2)=2, A(3)= 3, A(4)=6, A(5)=12
Seq after n>3 is [2^(n-3)] *3

Let us say x=3
so A(14)= [(2^13)*x]
and A(11)= [(2^8)*x]

ratio would be [(2^13)*x] / [(2^8)*x]
then it would be just [(2^11)]/[(2^8)]= 2^3
Show more

Hey AbhimanyuDhar,
Thanks for the insight. That is very helpful.
I just wanted to know how we know that after n>3, [2^(n-3)] *3 holds true for every term?
Is there a principle?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,963
Own Kudos:
1,117
Posts: 38,963
Kudos: 1,117
There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ 16 Nov 2024, 04:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109802 posts
Krunaal
Tuck School Moderator
853 posts