Last visit was: 25 Apr 2026, 19:08 It is currently 25 Apr 2026, 19:08
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
705-805 (Hard)|   Sequences|      
User avatar
shawndx
User avatar
Joined: 13 Oct 2011
Last visit: 20 May 2013
Posts: 9
Own Kudos:
136
 [48]
Given Kudos: 16
Products:
My Reviews
Posts: 9
Kudos: 136
 [48]
The sequence a(n) is defined so that, for all n is greater 08 Mar 2012, 22:14
5
Kudos
Add Kudos
43
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
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:

60% (02:49) correct 40% (02:39) wrong based on 643 sessions

History

Date
Time
Result
Not Attempted Yet
The sequence \(a_n\) is defined so that, for all \(n\) is greater than or equal to 3, \(a_n\) is the greater of \(a_{n-2} +1\) and \(a_{n-1}\). (If the two quantities are the same, then \(a_n\) is equal to either of them.) Which of the following values of \(a_1\) and \(a_2\) will produce a sequence in which no value is repeated?

A. \(a_1=-1\), \(a_2=-1.5\)
B. \(a_1=-1\), \(a_2=1\)
C. \(a_1=1\), \(a_2=-1\)
D. \(a_1=1\), \(a_2=1.5\)
E. \(a_1=1.5\), \(a_2=1\)
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
 [15]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
 [15]
The sequence a(n) is defined so that, for all n is greater 09 Mar 2012, 00:29
9
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
shawndx
The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n-2) +1) and (an-1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?

a) a1=-1, a2=-1.5
b) a1=-1, a2=1
c) a1=1, a2=-1
d) a1=1, a2=1.5
e) a1=1.5, a2=1

I am having trouble understanding what the question is asking and also solving it
Show more

Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally.

Given: \(a_n\) = Greater of \((a_{n-2} + 1, a_{n-1})\) (n is 3 or greater)
This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term)

If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'

So what can you deduce about \(a_1\) and \(a_2\)?
1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B)

2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\)

Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= -0.5)\) so reject it.
Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it.
Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it.

Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\).

OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D)
General Discussion
User avatar
shawndx
User avatar
Joined: 13 Oct 2011
Last visit: 20 May 2013
Posts: 9
Own Kudos:
136
Given Kudos: 16
Products:
My Reviews
Posts: 9
Kudos: 136
The sequence a(n) is defined so that, for all n is greater 09 Mar 2012, 15:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I do not understand the rule though... so if we were to just substitute values, how would one do that... if n were 3 or 4
User avatar
utkarshlavania
User avatar
Joined: 03 Sep 2010
Last visit: 03 Apr 2024
Posts: 10
Own Kudos:
22
 [3]
Given Kudos: 106
Posts: 10
Kudos: 22
 [3]
The sequence a(n) is defined so that, for all n is greater 10 Mar 2012, 01:38
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
shawndx
The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n-2) +1) and (an-1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?

a) a1=-1, a2=-1.5
b) a1=-1, a2=1
c) a1=1, a2=-1
d) a1=1, a2=1.5
e) a1=1.5, a2=1

I am having trouble understanding what the question is asking and also solving it

Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally.

Given: \(a_n\) = Greater of \((a_{n-2} + 1, a_{n-1})\) (n is 3 or greater)
This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term)

If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'

So what can you deduce about \(a_1\) and \(a_2\)?
1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B)

2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\)

Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= -0.5)\) so reject it.
Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it.
Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it.

Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\).

OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D)
Show more

@karishma
To be honest what is probability of such questions landing up on your gmat and on what level ...
I think, I would just flip the computer table and walk out rather than solve such types
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
 [1]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
 [1]
The sequence a(n) is defined so that, for all n is greater 11 Mar 2012, 02:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shawndx
I do not understand the rule though... so if we were to just substitute values, how would one do that... if n were 3 or 4
Show more

\(a_3\) depends on \(a_1\) and \(a_2\). Given the values of \(a_1\) and \(a_2\), you can find the values of all other terms.

Say if \(a_1 = 1\) and \(a_2 = 1.5\), then
\(a_3 = Greater (1 + 1, 1.5) = 2\)
\(a_4 = Greater (1.5+ 1, 2) = 2.5\) etc

On the other hand, if \(a_1 = 1\)
\(a_2 = 1.8\), then
\(a_3 = Greater (1 + 1, 1.8) = 2\)
\(a_4 = Greater (1.8+ 1, 2) = 2.8\) etc
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
The sequence a(n) is defined so that, for all n is greater 11 Mar 2012, 02:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
utkarshlavania


@karishma
To be honest what is probability of such questions landing up on your gmat and on what level ...
I think, I would just flip the computer table and walk out rather than solve such types
Show more

The question is not tough Utkarsh. I would suggest you to go one step at a time and try to figure it out. Such questions can be a part of actual GMAT and it's just a 700+, not exceptionally over the top. It looks complicated but most of the steps would be kind of intuitive after some practice. GMAT excels at testing simple concepts wrapped in a twisted package.
avatar
egiles
avatar
Joined: 01 Jun 2012
Last visit: 24 Jul 2014
Posts: 13
Own Kudos:
17
Given Kudos: 15
Location: United States
Concentration: Nonprofit
Schools: Ross '16 (II) Tuck '16 (M)
GMAT 1: 720 Q48 V43
GPA: 3.83
Schools: Ross '16 (II) Tuck '16 (M)
GMAT 1: 720 Q48 V43
Posts: 13
Kudos: 17
The sequence a(n) is defined so that, for all n is greater 04 Nov 2012, 15:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
shawndx
The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n-2) +1) and (an-1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?

a) a1=-1, a2=-1.5
b) a1=-1, a2=1
c) a1=1, a2=-1
d) a1=1, a2=1.5
e) a1=1.5, a2=1

I am having trouble understanding what the question is asking and also solving it

Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally.

Given: \(a_n\) = Greater of \((a_{n-2} + 1, a_{n-1})\) (n is 3 or greater)
This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term)

If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'

So what can you deduce about \(a_1\) and \(a_2\)?
1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B)

2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\)

Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= -0.5)\) so reject it.
Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it.
Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it.

Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\).

OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D)
Show more


Hi Karishma,

Thanks for your blog...I have been trying to solve every problem without using a pen per your advice and I am getting better at the quant section as a result.

Here is where I am confused about the above problem:

"If we want that every term in the sequence should be unique, \(n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'"

I'm reading the rule as \(A(n)\) is greater than \(A(n-2) + 1\). Above, you say they must be equal (at least that is how I'm reading it). Overall, the wording of this problem is awkward to me. I've never seen the phrase "...is the greater of". That just means it is great than, right?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
 [1]
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
 [1]
The sequence a(n) is defined so that, for all n is greater 04 Nov 2012, 21:29
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
egiles

"If we want that every term in the sequence should be unique, \(n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'"

I'm reading the rule as \(A(n)\) is greater than \(A(n-2) + 1\). Above, you say they must be equal (at least that is how I'm reading it). Overall, the wording of this problem is awkward to me. I've never seen the phrase "...is the greater of". That just means it is great than, right?
Show more


There are 2 diff things:

1. 'Is greater than'
x is greater than 4 and 5. This means x is a number greater than 5.

2. 'Is greater of'
x is greater of 4 and 5. This means x = 5.
Look at it this way: x = Greater of (4, 5)
First you find that which number is greater out of 4 and 5. x will be equal to that number.

x = Greater of (Last to last term + 1, Last term)
means find which is greater 'Last to last term + 1' or 'Last term'. X will be equal to that.
avatar
sagnik2422
avatar
Joined: 20 May 2014
Last visit: 20 Jan 2015
Posts: 27
Own Kudos:
20
Given Kudos: 1
Posts: 27
Kudos: 20
The sequence a(n) is defined so that, for all n is greater 03 Jul 2014, 09:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
shawndx
The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n-2) +1) and (an-1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?

a) a1=-1, a2=-1.5
b) a1=-1, a2=1
c) a1=1, a2=-1
d) a1=1, a2=1.5
e) a1=1.5, a2=1

I am having trouble understanding what the question is asking and also solving it

Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally.

Given: \(a_n\) = Greater of \((a_{n-2} + 1, a_{n-1})\) (n is 3 or greater)
This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term)

If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'

So what can you deduce about \(a_1\) and \(a_2\)?
1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B)

2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\)

Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= -0.5)\) so reject it.
Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it.
Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it.

Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\).

OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D)
Show more

KARISHMA (SORRY FOR CAPS JUST TRYING TO HIGHLIGHT WHERE MY QUESTION IS):

WHEN YOU SAY N IS 3 OR GREATER TOWARDS THE BEGINNING OF YOUR ANSWER HOW EXACTLY DID YOU DEDUCE THAT?
SECONDLY WHEN YOU ARE TESTING ANSWER CHOICES HOW EXACTLY DO YOU GET THE VALUE OF A3? FOR EXAMPLE WHEN YOU TEST CHOICE C HOW DID YOU GET A3 = 2?

THANKS :)
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
The sequence a(n) is defined so that, for all n is greater 03 Jul 2014, 19:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sagnik2422

KARISHMA (SORRY FOR CAPS JUST TRYING TO HIGHLIGHT WHERE MY QUESTION IS):

WHEN YOU SAY N IS 3 OR GREATER TOWARDS THE BEGINNING OF YOUR ANSWER HOW EXACTLY DID YOU DEDUCE THAT?
SECONDLY WHEN YOU ARE TESTING ANSWER CHOICES HOW EXACTLY DO YOU GET THE VALUE OF A3? FOR EXAMPLE WHEN YOU TEST CHOICE C HOW DID YOU GET A3 = 2?

THANKS :)
Show more

Since all previous quotes have a lighter background, it is easy to see where your question is so don't worry about that.

WHEN YOU SAY N IS 3 OR GREATER TOWARDS THE BEGINNING OF YOUR ANSWER HOW EXACTLY DID YOU DEDUCE THAT?

It is given in the question: "The sequence a(n) is defined so that, for all n is greater than or equal to 3".

SECONDLY WHEN YOU ARE TESTING ANSWER CHOICES HOW EXACTLY DO YOU GET THE VALUE OF A3? FOR EXAMPLE WHEN YOU TEST CHOICE C HOW DID YOU GET A3 = 2?

We know that An is greater of A(n-2) + 1 and A(n-1). This means An will be either (A(n-2)+ 1) or A(n-1), whichever is greater!
Now use options:

a) a1=-1, a2=-1.5

A3 = Greater of (A(1)+1, A(2))
A3 = Greater of (-1+1, -1.5)
A3 = Greater of (0, -1.5)
A3 = 0

c) a1=1, a2=-1

A3 = Greater of (A(1)+1, A(2))
A3 = Greater of (1+1, -1)
A3 = Greater of (2, -1)
A3 = 2

and so on...
User avatar
samusa
User avatar
Joined: 01 Nov 2013
Last visit: 30 Nov 2025
Posts: 240
Own Kudos:
1,068
Given Kudos: 410
GMAT 1: 690 Q45 V39
WE:General Management (Energy)
Products:
My Reviews
GMAT 1: 690 Q45 V39
Posts: 240
Kudos: 1,068
The sequence a(n) is defined so that, for all n is greater 16 Mar 2015, 02:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shawndx
The sequence \(a_n\) is defined so that, for all \(n\) is greater than or equal to 3, \(a_n\) is the greater of \(a_{n-2} +1\) and \(a_{n-1}\). (If the two quantities are the same, then \(a_n\) is equal to either of them.) Which of the following values of \(a_1\) and \(a_2\) will produce a sequence in which no value is repeated?

A. \(a_1=-1\), \(a_2=-1.5\)
B. \(a_1=-1\), \(a_2=1\)
C. \(a_1=1\), \(a_2=-1\)
D. \(a_1=1\), \(a_2=1.5\)
E. \(a_1=1.5\), \(a_2=1\)

I am having trouble understanding what the question is asking and also solving it
Show more

I solved the first option to get a hang of what kind of series comes out...
Quickly figured out that only in D it is possible \(a_{n-2} +1\) is always greater than \(a_{n-1}\) bcoz both entities are positive and \(a_2=1.5\) > \(a_1=1\)
User avatar
Lucky2783
User avatar
Joined: 07 Aug 2011
Last visit: 08 May 2020
Posts: 415
Own Kudos:
2,109
Given Kudos: 75
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT 1: 630 Q49 V27
Posts: 415
Kudos: 2,109
The sequence a(n) is defined so that, for all n is greater 21 Mar 2015, 08:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
shawndx
The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n-2) +1) and (an-1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?

a) a1=-1, a2=-1.5
b) a1=-1, a2=1
c) a1=1, a2=-1
d) a1=1, a2=1.5
e) a1=1.5, a2=1

I am having trouble understanding what the question is asking and also solving it

Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally.

Given: \(a_n\) = Greater of \((a_{n-2} + 1, a_{n-1})\) (n is 3 or greater)
This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term)

If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'

So what can you deduce about \(a_1\) and \(a_2\)?
1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B)

2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\)

Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= -0.5)\) so reject it.
Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it.
Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it.

Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\).

OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D)
Show more

I have noticed that manahattan gmat questions are very time intensive.
i would rather build the series for each of the given options A-E , atleast 2 elements .
User avatar
testcracker
User avatar
Joined: 24 Mar 2015
Last visit: 02 Dec 2024
Posts: 199
Own Kudos:
135
Given Kudos: 541
Status:love the club...
Posts: 199
Kudos: 135
The sequence a(n) is defined so that, for all n is greater 22 Mar 2018, 02:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasPrepKarishma
egiles

"If we want that every term in the sequence should be unique, \(n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'"

I'm reading the rule as \(A(n)\) is greater than \(A(n-2) + 1\). Above, you say they must be equal (at least that is how I'm reading it). Overall, the wording of this problem is awkward to me. I've never seen the phrase "...is the greater of". That just means it is great than, right?


There are 2 diff things:

1. 'Is greater than'
x is greater than 4 and 5. This means x is a number greater than 5.

2. 'Is greater of'
x is greater of 4 and 5. This means x = 5.
Look at it this way: x = Greater of (4, 5)
First you find that which number is greater out of 4 and 5. x will be equal to that number.

x = Greater of (Last to last term + 1, Last term)
means find which is greater 'Last to last term + 1' or 'Last term'. X will be equal to that.
Show more

hi mam

could you please tell me how to solve every problem without using a pen as egiles mentioned you said in your blog ?

thanks in advance, mam
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,413
Given Kudos: 485
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,413
The sequence a(n) is defined so that, for all n is greater 22 Mar 2018, 05:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatcracker2018
VeritasPrepKarishma
egiles

"If we want that every term in the sequence should be unique, \(n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'"

I'm reading the rule as \(A(n)\) is greater than \(A(n-2) + 1\). Above, you say they must be equal (at least that is how I'm reading it). Overall, the wording of this problem is awkward to me. I've never seen the phrase "...is the greater of". That just means it is great than, right?


There are 2 diff things:

1. 'Is greater than'
x is greater than 4 and 5. This means x is a number greater than 5.

2. 'Is greater of'
x is greater of 4 and 5. This means x = 5.
Look at it this way: x = Greater of (4, 5)
First you find that which number is greater out of 4 and 5. x will be equal to that number.

x = Greater of (Last to last term + 1, Last term)
means find which is greater 'Last to last term + 1' or 'Last term'. X will be equal to that.

hi mam

could you please tell me how to solve every problem without using a pen as egiles mentioned you said in your blog ?

thanks in advance, mam
Show more

Most actual GMAT questions can be solved using logic and reasoning and do not require equations, too many calculations etc. Usually when I answer questions on GMAT Club, I sit without pen and paper and get the answer orally. After that I start writing the explanation. Very rarely do I need to get up and get my notepad.
Though it is a skill one learns through practice. There are things that help such as using ratios, knowing multiplication tables etc.
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 25 Apr 2026
Posts: 5,986
Own Kudos:
5,859
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,986
Kudos: 5,859
The sequence a(n) is defined so that, for all n is greater 16 Mar 2024, 01:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shawndx
Given: The sequence \(a_n\) is defined so that, for all \(n\) is greater than or equal to 3, \(a_n\) is the greater of \(a_{n-2} +1\) and \(a_{n-1}\). (If the two quantities are the same, then \(a_n\) is equal to either of them.)

Asked: Which of the following values of \(a_1\) and \(a_2\) will produce a sequence in which no value is repeated?
A. \(a_1=-1\), \(a_2=-1.5\)
\(a_1=-1\), \(a_2=-1.5\), \(a_3=0[/m3], [m]a_4=0\) : Repeated : Incorrect
B. \(a_1=-1\), \(a_2=1\)
\(a_1=-1\), \(a_2=1\), \(a_3=1[/m3] Repeated : Incorrect\\
C. [m]a_1=1\), \(a_2=-1\)
\(a_1=1\), \(a_2=-1\), \(a_3=2[/m3], [m]a_4=2\) : Repeated : Incorrect
D. \(a_1=1\), \(a_2=1.5\)
\(a_1=1\), \(a_2=1.5\), \(a_3=2[/m3], [m]a_4=2.5\), \(a_3=3[/m3], [m]a_4=3.5\), Every term is .5 greater than previous term: repetition: Correct
E. \(a_1=1.5\), \(a_2=1\)
\(a_1=1.5\), \(a_2=1\), \(a_3=2.5[/m3], [m]a_4=2.5\) : Repeated : Incorrect

IMO D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,118
Posts: 38,986
Kudos: 1,118
The sequence a(n) is defined so that, for all n is greater 06 Oct 2025, 09:40
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
109830 posts
Krunaal
Tuck School Moderator
852 posts