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?
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.