After the first two terms in a sequence of numbers

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.

Answer

Assume first term as a and second term as b,

Third term = a + b

Fourth term = a + b + (a + b) = 2(a + b)

Fifth term = a + b + (a + b) + 2(a + b) = 4(a + b)

Therefore, if 4(a + b) = 12, it means a + b = 3

Hence, to determine whether fifth term is 12 or not, you need to know whether a + b is 3 or not.

Statement 1: The sum of the first 3 terms in the sequence is 6.

Therefore, a + b + (a + b) = 6

2(a + b) = 6

a + b = 3

As a + b = 3, we can say fifth term is 12. Hence, statement 1 is sufficient to answer the question.

Statement 2: The fourth term in the sequence is 6.

2(a + b) = 6

a + b = 3

As a + b = 3, we can say fifth term is 12. Hence, statement 2 is sufficient to answer the question.

The correct option is D.