In a certain sequence the difference between the (N-1)th : GMAT Data Sufficiency (DS)
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# In a certain sequence the difference between the (N-1)th

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

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22 Feb 2007, 20:55
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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
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22 Feb 2007, 21:05
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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
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06 Mar 2007, 15:20
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 ;)
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06 Mar 2007, 16:30
Prude_sb,

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

to:
a(n-1) = 2*a(n)
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06 Mar 2007, 19:09
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)
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09 Apr 2007, 22:28
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?
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09 Apr 2007, 22:50
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)
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18 May 2009, 20:06
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
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23 Aug 2009, 10:16
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
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19 Jun 2010, 12:09
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.
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In a certain sequence the difference between the (N-1)th [#permalink]

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19 Jun 2010, 12:48
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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.
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18 Sep 2010, 08:11
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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.
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18 Sep 2010, 08:20
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?
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18 Sep 2010, 08:23
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.
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18 Sep 2010, 08:36
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..
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18 Sep 2010, 08:40
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.....
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18 Oct 2010, 20:22
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.
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20 Oct 2010, 05:13
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.
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20 Oct 2010, 05:50
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...
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Re: In a certain sequence the difference between the (N-1)th [#permalink]

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