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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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Difficulty:

75% (hard)

Question Stats:

61% (02:46) correct
39% (01:57) wrong based on 160 sessions

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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.

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 ;)

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.

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.
_________________

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.
_________________

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

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

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

what about 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.
_________________

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 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.....
_________________

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.

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.
_________________

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

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27 Jan 2015, 03:53

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