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

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 ;)

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)

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)

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

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)

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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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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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.
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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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Wow, that is very important information. Thank you Bunuel.

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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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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