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

[AbeNeedsAnswers]

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.

D

Source: Official Guide 2020

[Jay@ManhattanReview]

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.

D

Source: Official Guide 2020

Say the first two terms are a and b, respectively.

Thus, the first five terms are

a, b, (a + b), 2(a + b), 4(a + b).

We have to determine whether 4(a + b) = 12 or (a + b) = 3.

Let's take each statement one by one.

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

=> The fourth term = 6
=> 2(a + b) = 6
a + b = 3. The answer is yes. Sufficient.

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

=> 2(a + b) = 6
a + b = 3. The answer is yes. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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[Ian Stewart]

If the sum of the first 3 terms is 6, then according to the definition of the sequence, the 4th term is 6. But then the fifth term is just the sum of the first 3 terms plus the 4th term, so is 6+6 = 12. Statement 1 is sufficient.

If the 4th term is 6, then by the definition of the sequence, the sum of the first three terms is 6. But then the fifth term is again 6+6 = 12, so Statement 2 is sufficient and the answer is D.

[[email protected]]

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

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Rich