In the infinite sequence S, each term Sn after S2 is equal to the sum

Question

In the infinite sequence S, each term  S_n  after  S_2  is equal to the sum of the two terms  S_{n– 1}  and  S_{n– 2} . If  S_1  is 4, what is the value of  S_2 ?

(1)  S_3 = 7  
(2)  S_4 = 10

I know that it is possible to find S2 with the first and the second statement (answer is D), it will equal 3.

My question is, how is it possible that in sequence the "order" goes like this: S1=4, S2=3, S3=7?
There is no sense in the order or no order at all? First term is larger than second and third is larger than second or first.

Isn't it relevant not just to find number solution but also check if it fits the common rule of sequence?

I would appreciate as detailed explanation as possible! Thanks a lot in advance!

-Maria

Bunuel · Answer

The sequence is 4, 3, 7, 10, 17, 27, ...

The above sequence follows the rule that each term Sn  after S2  is equal to the sum of the two terms S(n-1) and S(n-2):
S3 = S2 + S1 --> 7 = 3 + 4;
S4 = S3 + S2 --> 10 = 7 + 2;
S5 = S3 + S3 --> 17 = 10 + 7;
...

Gonner · Answer

Hi Bunuel,
Statement 1 alone is sufficient i get that but how is statement 2 alone sufficient, 
S4=S3+S2 we need to use statement 1 to know the value of S3.
So shouldn't the answer be A.

Bunuel · Answer

(2) S4 = 10 and S1 = 4.

S4 = S3 + S2 = (S2 + S1) + S2
10 = (S2 + 4) + S2
S2 = 3.

Hope it's clear.

EMPOWERgmatRichC · Answer

Hi All,

This DS question involves a rare sequence called a "Fibonacci" sequence (but not the "classic" Fibonacci sequence that you might have learned in School).

In a Fibonacci sequence, adding two consecutive 'terms' will give you the value of the "next" term.....

The classic Fibonacci is.....1, 1, 2, 3, 5, 8, 13, 21, 34 etc.
eg
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
etc.

The prompt describes this math concept using sequence "notation", so if you see this pattern in another question, you now know what it translates into mathematically.

In this prompt, we have the description of a Fibonacci, but it does NOT start with two 1s. We're told that the first term is a 4. We're asked for the value of the second term.

Fact 1: S3 = 7

This tells us the third term is 7, so we can create the following equation....

(1st term) + (2nd term) = (3rd term)
(4) + (X) = 7
X = 3, so we know the value of the second term.
Fact 1 is SUFFICIENT

Fact 2: S4 = 10

This tells us the fourth term is 10. While many Test Takers might *think* that this is insufficient, with a bit of work, you might recognize an Algebra pattern...

(1st term) + (2nd term) = (3rd term)
(4) + (X) = (Y)

(2nd term) + (3rd term) = (4th term)
(X) + (Y) = 10

Here, we have a two-variable algebra "system", so we CAN solve it (and figure out the value of BOTH the second and third terms.
Fact 2 is SUFFICIENT.

Final Answer:  D

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

MariaVorop · Answer

Oh, okay, thanks a lot!
Haven't recognized that rule.

But basically any order or rule for the order of sequence can be made up.

Best,
Maria

EMPOWERgmatRichC · Answer

Hi Maria,

Yes, questions that use sequence notation are 'made up' and can involve any manner of Arithmetic and Algebra. In most cases, you're given the "rules" of the sequence and then you're asked to perform some calculation. In rarer cases (certain types of DS questions), you're told that there's a sequence, but you're not told the exact "rules", so you have to try to get to the correct answer with logic and pattern-matching skills.

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

chetan2u · Answer

Hi..
s1 is given.. and each term after 1st and 2nd can be found by adding the trevious two terms..
 this means all terms can be finally written in terms of s1 and s2.. ..
therefore any other value in the sequence can help us in finding s2..
(1) S3 = 7 
(2) S4 = 10..

both statement give us another value to work on.. 
each is suff..
ans D

asethi · Answer

(1) S3 = 7 
 S3=S2+S1; 7=S2+4...Suff
(2) S4 = 10 
 S4=S3+S2 ;10=S3+S2 ......(a)
 S3=S2+S1; S3=S1+4.....(b)
 From the eqs (a) and (b) .....Suff

Ans: D

Divyadisha · Answer

(1) S3 = 7
S3=S2+S1
We know the values of S3 and S1. S2 can be calculated. Sufficient

(2) S4 = 10
S4= S3+S2
S4= S2+S1+S2 (S3 can be written as S2+S1)
S4= 2S2 +S1
We know the values of S4 and S1 and hence S2 can be calculated.

D is the answer

pran1pran1 · Answer

This is probably not useful, but I like to write the sequence down in ABCD terms for this question.

For e.g

s1,s2,s3,s4,s5 = a,b,c,d,e,

We know that c=b+a and d=b+c and so on.

Now if a=4 and we are trying to find what b =, let's look at our two data points.

1) s3 = 7 ( So c = 7)
Since c=b+a and c=7, b=4 we can solve this by 7=b+4, B=3

2) s4=10 (So d=10) 
Since d=b+c and we already know that c=b+a (As per the question statement, not the data point) We can calculate this backwards

D=10
D=b+c
C=b+a

Therefore D=(b+a)+B
10=b+4+b or 10=4+2b
10-4=2b
6=2b
6/2=b
b=3

Refer to your S sequence and see if you can get the right answer

ManifestDreamMBA · Answer

S_1  = 4
 S_2  = ?

Statement 1
 S_3 = 7 
 S_3 = S_2 + S_1 
 7 = S_2 + 4 
 S_2 = 3 
Sufficient

Statement 2
 S_4 = 10 
 S_4 = S_3 + S_2 
 S_3 = S_2 + S_1 
 S_4 = S_2 + S_1 + S_2 
 S_4 = 2S_2 + S_1 
 10 = 2S_2 + 4 
 S_2=3 
Sufficient

In the infinite sequence S, each term Sn after S2 is equal to the sum

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GMAT Data Sufficiency (DS) Questions

In the infinite sequence S, each term Sn after S2 is equal to the sum

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