What is the 1st term in sequence S ?

Question stem. What's the value of \(S_1\) ?

From statement 1:

\(S_3 = 2\).
Clearly Insufficient.

From statement 2:

\(S_2 = 2S_1\)
\(S_3 = 3S_2\)
All 3 unknows.
Insufficient.

Combining both:

\(S_3 = 2\)
Then \(S_2\) = 1.
So, \(S_1\) = 1/2.

C is the answer.

(1) The 3rd term in S is 2. - NS: S3 =2
(2) The 2nd term in S is twice the 1st, and the 3rd term is three times the 2nd. -NS : ==> S3 =3S2 =6S1
(1+2) Sufficient : as S3 =2 , Hence, S1 = \(\frac{2}{6} = \frac{1}{3}\) ..... Hence Ans C

No need to solve completely as this is a DS question!

Stmt 1: S3 = 2, No info on S1, Insufficient. Eliminate A,D
Stmt 2: S2 = 2*S1, S3 = 3*S2, No values given for any term, so cannot find out value of S1, Insufficient. Eliminate B

Combined: We can find the value of S1, by back tracking through the three equations from Stmts 1 and 2. Hence Sufficient.

Option C

Given that \(S_3 = 2\). We cannot figure any specific value for S1

Insufficient.

We look at Statement 2) it tells us\(S_2 = 2*S_1\) and \(S_3 = 3*S_2\).

Still insufficient as I have 2 equations and 3 variables.

Combining both we have one variable that can be substituted to provide a numerical value. This numerical value can then be substituted in the other equation.

C

Statement 1 This only gives us the value of 3rd term and no relation whatsoever to the 1st term of the sequence. There is no way we can find the first term of the sequence using this info. Hence, this is INSUFFICIENT

Statement 2 This gives us relation about the 3 terms. Now we know the first 3 terms will look somewhat like this--> a, 2a, 6a. But we have no clue about the value of 'a' here. Hence, this alone is INSUFFICIENT

Statement 1 + Statement 2 Now we know that 6a=2. Hence we can find the value of a which is 1/3. hence we get a unique numerical value. hence this is SUFFICIENT


Hence, the answer is C

Target question: What is the 1st term in sequence S ?

Statement 1: The 3rd term in S is 2
Since we're not given any information about the NATURE of the sequence, there's no way to answer the target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: The 2nd term in S is twice the 1st, and the 3rd term is three times the 2nd.
Great, we're given information about the NATURE of the sequence, but we aren't given the VALUE of any terms.
For example, consider these two possible cases that satisfy statement 2:
Case a: The first 3 terms are: {1, 2, 6....}. In this case, the answer to the target question is the 1st term is 1
Case b: The first 3 terms are: {3, 6, 18....}. In this case, the answer to the target question is the 1st term is 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the 3rd term in S is 2
Statement 2 tells us that the 3rd term is three times the 2nd. So, if the 3rd term is 2, then the 2nd term must be 2/3
Statement 2 also tells us that the 2nd term in S is twice the 1st. So, if the 2nd term is 2/3, then the 1st term must be 1/3
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

Hello gmatbusters,

in the question is not said, that there are only 3 terms.
Do I have to assume so?

I thought it would be E because there was no information about the total number of terms

Hey gzuz, Let me try to answer.
The minimum number of terms you need to determine the kind of series (AP, GP or HP).
Hence when 2 statements are combined, we are able the find the first term.
Hence C is the answer.

The target question only asks us to determine "the 1st term in sequence S"
So, the total number of terms in the sequence has no bearing on our ability to answer the target question.

Cheers,
Brent

(1) Merely knowing the third term does not tell us anything about the first term. Insufficient.
(2) 1st term = x, 2nd term = 2x, 3rd term = 6x, does not give us value of x. Insufficient.

Combining the two,
3rd term = 6x = 2 therefore, x = 1/3
Therefore, the first term is equal to 1/3

Hence, we can only answer the questions using both the statements together, option C.

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