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

Question

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

ScottTargetTestPrep · Accepted Answer

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

chetan2u · Answer

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

Archit3110 · Answer

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

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made, 
Rich

brains · Answer

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

Hence answer must be D

AnirudhaS · Answer

(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,...

Answer:  D

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=msw0iswVN14

GmatKnightTutor · Answer

Post below.

Ibrahim13 · Answer

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.

Posted from my mobile device

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=Zq63woH6_OA

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=b8m2UcHGK3Q Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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