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# After the first two terms in a sequence of numbers, each term in the

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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
Bunuel wrote:
After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

DS92602.01
OG2020 NEW QUESTION

1st term = a
2nd term = b
so 3rd term ; a+b= 6
4th term ; 6+a+b =
5th term ; 6+6+a+b; 12+a+b

#2 to check 5th term = 12 = 4th term + 3rd term + a+b
4th term ; 3rd term + a+b = 6
so 5th term ; 6+3rd term + a+b
sufficient
IMO D
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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
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Hi All,

We're told that after the first two terms in a sequence of numbers, each term in the sequence is formed by adding ALL of the preceding terms. We're asked if 12 is the fifth term in the sequence? This is a YES/NO question and can be approached with some basic Arithmetic and note-taking.

(1) The sum of the first 3 terms in the sequence is 6.

With the information in Fact 1, we don't know exactly what those three terms are (they could be 0, 3, 3 or 1, 2, 3, for example), but that doesn't matter, since we can now determine how the sequence proceeds from there...
4th term = sum of the first 3 terms = 6
5th term = sum of the first 4 terms = 6+6 = 12
Thus, the answer to the question is YES.
Fact 1 is SUFFICIENT

(2) The fourth term in the sequence is 6.

The information in Fact 2 defines the same pattern we deduced in Fact 1:
4th term = sum of the first 3 terms = 6
5th term = sum of the first 4 terms = 6+6 = 12
Fact 2 is SUFFICIENT

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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
I tried with a logical approach:
If first term is x and second is y, then third term is x+y
Fourth term is 2 (x+y)
Fifth term is 2*2(x+y)
We can see a pattern after first three terms, the following term is double of its preceding term.
Statement-1 : The sum of first 3 terms is 6 , then from Q.stem we know fourth term should be double of that. So only combination is 1,2,3. So fourth term is 6 and fifth term is 12. Hence Sufficient

Statement-2 : The fourth term in the sequence is 6.
This is apparently same as Statement 1 and we found out that fifth term should be double of fourth term 6 . So 12 is there in sequence.. Sufficient

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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

Both statements convey the same message, that the 4th term is 6. Because if the sum of the first 3 terms is 6, then the 4th term MUST be 6 according to the problem.

So answer is D or E

Now, regardless of the first three terms, if the 4th term is 6th, then the following sequence must be like this {a,b,c,6,12,24.....}, where a,b,c are the first three terms.
For e.g. - the set can be {1,2,3,6,12,24,...} or {0,3,3,6,12,24,...} but whatever the values of a,b, c are; from the 4th term the sequence must be 6,12,24,...

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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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After the first two terms in a sequence of numbers, each term in the [#permalink]
Post below.

Originally posted by GmatKnightTutor on 27 Jan 2021, 00:54.
Last edited by GmatKnightTutor on 11 Oct 2021, 19:08, edited 3 times in total.
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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
Eg even consecutive integers
2,4,6,8,10,12,14,16,18,20
a=2 b=4
Third term= after the first two terms I.e 6+8=12
Fourth term = 14+10=24
Fifth term = 24+12= 36
The sum of the first 3 terms
2+4+6=12
The fourth term in the sequence 24. Both statements are not sufficient to answer the question.

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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
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Bunuel wrote:
After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

(1) The sum of the first 3 terms in the sequence is 6.
(2) The fourth term in the sequence is 6.

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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
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Re: After the first two terms in a sequence of numbers, each term in the [#permalink]
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