Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 Jun 2016, 22:44

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

In a certain sequence the difference between the (N-1)th

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager
Joined: 12 Feb 2006
Posts: 115
Followers: 1

Kudos [?]: 56 [0], given: 0

In a certain sequence the difference between the (N-1)th [#permalink]

Show Tags

22 Feb 2007, 21:55
5
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

59% (02:44) correct 41% (01:57) wrong based on 148 sessions

HideShow timer Statistics

In a certain sequence the difference between the (N-1)th and Nth element equals the Nth element (N is any positive integer). What is the fourth element of this sequence?

(1) The first element of the sequence is 1.
(2) The third element of the sequence is 1/4.
[Reveal] Spoiler: OA
Senior Manager
Joined: 12 Mar 2006
Posts: 366
Schools: Kellogg School of Management
Followers: 3

Kudos [?]: 57 [2] , given: 3

Show Tags

22 Feb 2007, 22:05
2
KUDOS
a(n) = nth element in the sequence

this means that a(n-1) - a(n) = a(n) => a(n-1) = 2*a(n) => a(n) = a(n-1)/2

so if we go on substituting this formula until n = 1 on the RHS we get

a(n) = a(1)/2^(n-1)

so a(4) = a(1)/2^3

so either stat1 or stat2 can be used to get the ans

my ans is D
Intern
Joined: 02 Mar 2007
Posts: 30
Followers: 0

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

Show Tags

06 Mar 2007, 16:20
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra ;)
Director
Joined: 12 Jun 2006
Posts: 532
Followers: 2

Kudos [?]: 80 [0], given: 1

Show Tags

06 Mar 2007, 17:30
Prude_sb,

Please explain how you went from:
a(n-1) - a(n) = a(n)

to:
a(n-1) = 2*a(n)
Senior Manager
Joined: 12 Mar 2006
Posts: 366
Schools: Kellogg School of Management
Followers: 3

Kudos [?]: 57 [0], given: 3

Show Tags

06 Mar 2007, 20:09
ggarr wrote:
Prude_sb,

Please explain how you went from:
a(n-1) - a(n) = a(n)

to:
a(n-1) = 2*a(n)

a(n-1) - a(n) = a(n)

=> a(n-1) = a(n) + a(n)
=> a(n-1) = 2*a(n)
Director
Joined: 19 Mar 2007
Posts: 524
Followers: 3

Kudos [?]: 24 [0], given: 0

Show Tags

09 Apr 2007, 23:28
prude_sb wrote:
a(n) = nth element in the sequence

this means that a(n-1) - a(n) = a(n) => a(n-1) = 2*a(n) => a(n) = a(n-1)/2

so if we go on substituting this formula until n = 1 on the RHS we get

a(n) = a(1)/2^(n-1)

so a(4) = a(1)/2^3

so either stat1 or stat2 can be used to get the ans

my ans is D

Could anybody please explain how Prude has obtained powers in the equation marked above?
SVP
Joined: 01 May 2006
Posts: 1798
Followers: 9

Kudos [?]: 132 [0], given: 0

Show Tags

09 Apr 2007, 23:50
nick_sun wrote:
prude_sb wrote:
a(n) = nth element in the sequence

this means that a(n-1) - a(n) = a(n) => a(n-1) = 2*a(n) => a(n) = a(n-1)/2

so if we go on substituting this formula until n = 1 on the RHS we get

a(n) = a(1)/2^(n-1)

so a(4) = a(1)/2^3

so either stat1 or stat2 can be used to get the ans

my ans is D

Could anybody please explain how Prude has obtained powers in the equation marked above?

Once we have a(n) = a(n-1)/2, we can calculate the relation in term n-2, n-3.... 1.

Notice that it's geometry sequence with r=1/2. Formulas helps us to conclude directly.

This is a full detailed way to arrive at the answer

a(n)
= a(n-1)/2 >>> with n-1
= 1/2 * (a(n-2)/2) >>> with n-2
= 1/2 * 1/2 * (a(n-3)/2) >>> with n-3
= (1/2)^3 * a(n-3)
= (1/2)^p * a(n-p) >>> with n-p

Then, if p = n-1, we have:
a(n)
= (1/2)^p * a(n-p)
= (1/2)^(n-1) * a(n-(n-1))
= (1/2)^(n-1) * a(1)
Intern
Joined: 28 Mar 2009
Posts: 23
Followers: 1

Kudos [?]: 19 [0], given: 0

Re: Sequence DS [#permalink]

Show Tags

18 May 2009, 21:06
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks
Intern
Joined: 07 Jan 2005
Posts: 8
Location: New York
Followers: 0

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

Re: Sequence DS [#permalink]

Show Tags

23 Aug 2009, 11:16
Good try (I had not thought the solution could be the second sequence too)

BUT I see you missed a stated fact
N is a positive number.This fact rejects your second sequence ( 0 is neither + or -ve)

mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks
Intern
Joined: 09 Dec 2009
Posts: 34
Followers: 0

Kudos [?]: 11 [0], given: 7

Show Tags

19 Jun 2010, 13:09
ppetkov wrote:
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra

Is this correct? Can someone confirm? This could save us some time in DS questions.
Math Expert
Joined: 02 Sep 2009
Posts: 33489
Followers: 5925

Kudos [?]: 73353 [1] , given: 9902

In a certain sequence the difference between the (N-1)th [#permalink]

Show Tags

19 Jun 2010, 13:48
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
JoyLibs wrote:
ppetkov wrote:
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra

Is this correct? Can someone confirm? This could save us some time in DS questions.

Yes it's correct.

For arithmetic (or geometric) progression if you know:

- any particular two terms,
- any particular term and common difference (common ratio),
- the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.
_________________
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 218

Kudos [?]: 1446 [1] , given: 235

Re: Sequence DS [#permalink]

Show Tags

18 Sep 2010, 09:11
1
KUDOS
bz9 wrote:
Here is another sequence question I could use some help on. I guess the answer correctly, but I'm having a hard time wrapping my head around sequence questions.

In a certain sequence the difference between the (N-1)th and Nth element equals the Nth element (N is any positive integer). What is the fourth element of this sequence?

1. The first element of the sequence is 1.
2. The third element of the sequence is 1/4.

There is no information of total number of terms.

$$T_{N-1} - T_{N} =T_{N}$$

$$T_{N-1} = T_{N} +T_{N}$$

$$T_{N-1} = 2*T_{N}$$

1. The first element is 1

=> $$T_1 = 2* T_2$$ => $$T_1 = 2^2 * T_3$$ => $$T_1 = 2^3 * T_4$$
Since T_1 is given, this is sufficient.

2. $$T_3 = 1/4$$ using same reason above this is also sufficient.

Hence D

Moreover
$$T_{N-1} = 2*T_{N}$$ represents GP series with ratio =1/2. We only need to know the value of any term to find the whole series.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 690
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 129 [0], given: 15

Re: Sequence DS [#permalink]

Show Tags

18 Sep 2010, 09:20
hoping_for_stern wrote:
Good try (I had not thought the solution could be the second sequence too)

BUT I see you missed a stated fact
N is a positive number.This fact rejects your second sequence ( 0 is neither + or -ve)

mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks

Why does N being a positive number mean that the sequence consists of positive numbers? Isn't n just the index? Or should the statement have been a_n is positive? Also when it says the difference between an and an-1, people have used
an-1 - an = an

an - an-1 = an => in which case an-1 would be 0 and that situation is perhaps avoided by saying an is positive?
_________________

Consider kudos, they are good for health

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 218

Kudos [?]: 1446 [0], given: 235

Re: Sequence DS [#permalink]

Show Tags

18 Sep 2010, 09:23
mainhoon wrote:
hoping_for_stern wrote:
Good try (I had not thought the solution could be the second sequence too)

BUT I see you missed a stated fact
N is a positive number.This fact rejects your second sequence ( 0 is neither + or -ve)

mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks

Why does N being a positive number mean that the sequence consists of positive numbers? Isn't n just the index? Or should the statement have been a_n is positive? Also when it says the difference between an and an-1, people have used
an-1 - an = an

an - an-1 = an => in which case an-1 would be 0 and that situation is perhaps avoided by saying an is positive?

if $$a_{n-1} = 0$$ => the whole sequence is 0.....but when you will use the statements, the value of terms are non-zero hence you $$a_{n-1} = 0$$ is not true.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 690
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 129 [0], given: 15

Re: Sequence DS [#permalink]

Show Tags

18 Sep 2010, 09:36
I have a distinct feeling that the original question clearly ruled out an = 0, that is was not saying N is positive (as posted here).. But now that brings up an interesting question - can the stem conflict with the statements? In other words do we have to take the statements to be true?

There was another example where the statements were not needed to answer the question, just the stem was enough.. xy<yz<0..
_________________

Consider kudos, they are good for health

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2797
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 218

Kudos [?]: 1446 [0], given: 235

Re: Sequence DS [#permalink]

Show Tags

18 Sep 2010, 09:40
mainhoon wrote:
I have a distinct feeling that the original question clearly ruled out an = 0, that is was not saying N is positive (as posted here).. But now that brings up an interesting question - can the stem conflict with the statements? In other words do we have to take the statements to be true?

There was another example where the statements were not needed to answer the question, just the stem was enough.. xy<yz<0..

I dont think in gmat you will get such questions.....
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Joined: 19 Feb 2010
Posts: 401
Followers: 22

Kudos [?]: 159 [0], given: 76

Show Tags

18 Oct 2010, 21:22
Bunuel wrote:
JoyLibs wrote:
ppetkov wrote:
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra

Is this correct? Can someone confirm? This could save us some time in DS questions.

Yes it's correct.

For arithmetic (or geometric) progression if you know:

- any particular two terms,
- any particular term and common difference (common ratio),
- any particular term and the formula for n_th term,
- the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.

Wow, that is very important information. Thank you Bunuel.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6666
Location: Pune, India
Followers: 1827

Kudos [?]: 11091 [0], given: 218

Re: Sequence DS [#permalink]

Show Tags

20 Oct 2010, 06:13
Expert's post
mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks

It is given in the question that t(n-1) - t(n) = t(n), so t(n) = t(n-1)/2
Every subsequent term should be half of the previous term. Statement II does not lead to 0, 0, 0.25, 0.5 since the difference between 3rd and 4th terms is 0.25 which should be equal to the fourth term but it is not. The fourth term is 0.5 here. It only leads to the first sequence and hence statement II alone is sufficient.

Statements never ever contradict the data of the question stem or each other for that matter. They only provide additional information or repeat what we already have.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 25 Aug 2010
Posts: 98
Followers: 1

Kudos [?]: 4 [0], given: 1

Re: Sequence DS [#permalink]

Show Tags

20 Oct 2010, 06:50
very good post....

first time i tried to go with the numbers and end up with a mess...

If i go and try to put some numbers in it, i would end up with the mess...

a(n_1) - a(n) = a(n)

==> a(n_1) = 2* a(n))
a(n-2) = 2* a(n_1)
==> 2*2* a(n)

----> I can get some where in the seq the value for (1) option and (2) option...
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 10164
Followers: 480

Kudos [?]: 124 [0], given: 0

Re: In a certain sequence the difference between the (N-1)th [#permalink]

Show Tags

27 Jan 2015, 04:53
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.
_________________
Re: In a certain sequence the difference between the (N-1)th   [#permalink] 27 Jan 2015, 04:53

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
3 An arithmetic progression is a sequence in which the difference of any 3 05 Mar 2016, 13:21
24 The next number in a certain sequence is defined by multiply 5 12 Sep 2013, 06:13
66 In a certain year, the difference between Mary's and Jim's 25 25 Nov 2007, 20:12
4 What is the difference between the lengths of diagonals of 8 15 Nov 2007, 08:43
18 In a certain year, the difference between Mary's and Jim's a 7 25 Apr 2007, 07:54
Display posts from previous: Sort by

In a certain sequence the difference between the (N-1)th

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.