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

Question

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.

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

sudhir18n · Answer

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.

gmatprep2011 · Answer

@sudhir18n

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

fluke · Answer

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.

nitin6305 · Answer

I could get to the answer, but took almost 2:30 to evaluate both the options. Can anyone please provide a quicker solution?

BankerRUS · Answer

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.

Bunuel · Answer

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.

CIyer · Answer

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!

gauravkaushik8591 · Answer

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?

Bunuel · Answer

This question is marked as poor quality. So, you could ignore it. Check similar questions in my post above.

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

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