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

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New post 26 Apr 2019, 02:56
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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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OG2020 NEW 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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New post 26 Apr 2019, 04:44
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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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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?

Now, we are just looking at fifth term, so we can write the first five terms, when first two terms are x and y
So, x, y, ... Third term=(x+y)... fourth term=(x+y)+x+y=2(x+y), and fifth term = 4(x+y)..
The general term is \(2^{n-3}(x+y)\), so fifth term = \(2^{5-3}(x+y)=4(x+y)\)

1. The sum of the first 3 terms in the sequence is 6.
so sum of the first 3 terms in the sequence=4th term = \(2^{4-3}(x+y)=2(x+y)=6.......x+y=3\)
So, 4(x+y)=483=12
suff

2. The fourth term in the sequence is 6.
Same as statement I
Suff
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Re: After the first two terms in a sequence of numbers, each term in the  [#permalink]

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New post 27 Apr 2019, 07:57
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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New post 12 May 2019, 19:08
1
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



If we can determine the 5th term, then we can determine whether it’s 12 or not. To determine the 5th term, we either need to know the first two terms (since once we know those two terms, then we can determine any other terms) or the sum of the first 3 terms and the 4th term (since the 5th term is the sum of the first 4 terms).
Statement One Alone:

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

Since the 4th term is the sum of the first 3 terms, so the 4th term is also 6 and thus the 5th term = the 4th term + the sum of the first 3 terms = 6 + 6 = 12. Statement one alone is sufficient.

Statement Two Alone:

The fourth term in the sequence is 6.

Since the 4th term is the sum of the first 3 terms, so the sum of the first 3 terms is also 6 and thus the 5th term = the 4th term + the sum of the first 3 terms = 6 + 6 = 12. Statement two alone is sufficient.

Answer: 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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New post 15 May 2019, 20:41
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

Final Answer:

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Re: After the first two terms in a sequence of numbers, each term in the   [#permalink] 15 May 2019, 20:41
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