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S is an infinite sequence, in which the value of a

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S is an infinite sequence, in which the value of a [#permalink] New post 23 Sep 2011, 22:23
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S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?

(1) The 1st term is 1.
(2) The 3rd term is 3.
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Re: DS Question - Sequences [#permalink] New post 23 Sep 2011, 23:08
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gmatprep2011 wrote:
S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?

(1) The 1st term is 1.
(2) The 3rd term is 3.


St1: t1 = 1
Let t2 = x
t3 = t2-t1= x-1 ( difference between the two preceding members of the sequence)
t4 = t3-t2 = x-1-x = -1
t5 = t4-t3 = -1-x+1= -x
t6 = t5 -t4 = -x+1 = 1-x
t7 = t6-t5 = 1-x+x = 1

If u carefully see , this follows are particular pattern; first 3 terms , then next 3 ( but negative).. this is symmetry .. and will continue ( t7 will start again with 1)
hence t 7 = 1
t 13 = 1
t19=1
t25= 1
t31= 1
t 37= 1
t 43 = 1

Hence statement 1 : sufficient

St 2: not much of help .

hence its A.
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Re: DS Question - Sequences [#permalink] New post 23 Sep 2011, 23:16
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@sudhir18n

It does not mention whether second term minus first term or vice versa... Can it be C or E then?
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Re: DS Question - Sequences [#permalink] New post 24 Sep 2011, 05:15
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gmatprep2011 wrote:
@sudhir18n

It does not mention whether second term minus first term or vice versa... Can it be C or E then?


That's a valid point. However, it should also mention n>=3, because we need at least two terms to even execute this condition.

With the above assumption, "C" would be the answer.

But, if the question were written like this:

S is an infinite sequence, in which each term S_n=S_{(n-1)}-S_{(n-2)}, such that n>=3. What is the value of the 43rd member of the sequence?

1. S_1=1
2. S_3=3

Answer would be A as nicely explained by sudhir18n.
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Re: DS Question - Sequences [#permalink] New post 08 May 2013, 19:45
sudhir18n wrote:
gmatprep2011 wrote:
S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?

(1) The 1st term is 1.
(2) The 3rd term is 3.


St1: t1 = 1
Let t2 = x
t3 = t2-t1= x-1 ( difference between the two preceding members of the sequence)
t4 = t3-t2 = x-1-x = -1
t5 = t4-t3 = -1-x+1= -x
t6 = t5 -t4 = -x+1 = 1-x
t7 = t6-t5 = 1-x+x = 1

If u carefully see , this follows are particular pattern; first 3 terms , then next 3 ( but negative).. this is symmetry .. and will continue ( t7 will start again with 1)
hence t 7 = 1
t 13 = 1
t19=1
t25= 1
t31= 1
t 37= 1
t 43 = 1

Hence statement 1 : sufficient

St 2: not much of help .

hence its A.


I could get to the answer, but took almost 2:30 to evaluate both the options. Can anyone please provide a quicker solution?
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Re: DS Question - Sequences [#permalink] New post 28 May 2013, 07:35
With the above assumption, "C" would be the answer.

But, if the question were written like this:

S is an infinite sequence, in which each term S_n=S_{(n-1)}-S_{(n-2)}, such that n>=3. What is the value of the 43rd member of the sequence?

1. S_1=1
2. S_3=3


Why would the answer be c? you could have a sequence: 1,-2,3 or you could have 1,4,3. So the fourth term would be different in these two cases!! What is the source of this question??
Answer would be A as nicely explained by sudhir18n.[/quote]
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Re: S is an infinite sequence, in which the value of a [#permalink] New post 28 May 2013, 09:13
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gmatprep2011 wrote:
S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?

(1) The 1st term is 1.
(2) The 3rd term is 3.


Similar questions to practice:
if-s-is-the-infinite-sequence-s1-9-s2-99-s3-999-sk-10-k-127798.html
an-infinite-sequence-of-positive-integers-is-called-a-127696.html
an-infi-nite-sequence-of-positive-integers-is-called-a-127496.html

Hope it helps.
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Re: S is an infinite sequence, in which the value of a [#permalink] New post 03 Jul 2013, 07:04
Hello.. Can we say that as the question stands now, the answer is "E". I feel so as there is no way to know whether t3= t2-t1 or t3= t1-t2.... Thanks in advance!
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S is an infinite sequence, in which the value of a [#permalink] New post 21 Sep 2014, 08:56
Bunuel wrote:
gmatprep2011 wrote:
S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?

(1) The 1st term is 1.
(2) The 3rd term is 3.


Similar questions to practice:
if-s-is-the-infinite-sequence-s1-9-s2-99-s3-999-sk-10-k-127798.html
an-infinite-sequence-of-positive-integers-is-called-a-127696.html
an-infi-nite-sequence-of-positive-integers-is-called-a-127496.html

Hope it helps.


Bunuel,

Why do we assume here that the difference = a2 - a1? couldn't it be equal to a1-a2 also?

First term is 1 , 3rd term is 3.

So the second term can be 4 OR -2, isn't it?

when you say 'difference between two numbers' it can either be x-y or y-x, right?
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Re: S is an infinite sequence, in which the value of a [#permalink] New post 21 Sep 2014, 10:41
Expert's post
gauravkaushik8591 wrote:
Bunuel wrote:
gmatprep2011 wrote:
S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?

(1) The 1st term is 1.
(2) The 3rd term is 3.


Similar questions to practice:
if-s-is-the-infinite-sequence-s1-9-s2-99-s3-999-sk-10-k-127798.html
an-infinite-sequence-of-positive-integers-is-called-a-127696.html
an-infi-nite-sequence-of-positive-integers-is-called-a-127496.html

Hope it helps.


Bunuel,

Why do we assume here that the difference = a2 - a1? couldn't it be equal to a1-a2 also?

First term is 1 , 3rd term is 3.

So the second term can be 4 OR -2, isn't it?

when you say 'difference between two numbers' it can either be x-y or y-x, right?


This question is marked as poor quality. So, you could ignore it. Check similar questions in my post above.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: S is an infinite sequence, in which the value of a   [#permalink] 21 Sep 2014, 10:41
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