Arrange the statements in proper logical sequence.
A. The pattern continues by multiplying the number by 3.
B. Therefore, the next number must be 324.
C. The given series is 4, 12, 36, 108, ?
D. Middle term is the geometric mean of its previous and next term.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → C, A, B, D
The argument starts from the series that is given, reads its pattern and draws the conclusion; statement D, a general property of a geometric progression, then confirms the completed series.
C. The given series is 4, 12, 36, 108, ? — comes first, since nothing can be said about the series before it is stated.
A. The pattern continues by multiplying the number by 3. — the pattern read from the series:
\(4\times3=12\), \(12\times3=36\), \(36\times3=108\)
B. Therefore, the next number must be 324. — the conclusion from A; the word “Therefore” shows that it follows a reason:
\(108\times3=324\)
D. Middle term is the geometric mean of its previous and next term. — the property of every series in which each term is a fixed multiple of the one before (a geometric progression), so it closes the argument:
With 324 in place, 108 is the geometric mean of 36 and 324: \(\sqrt{36\times324}=6\times18=108\)
Note: One can argue that statement D could come second, giving C, D, A, B (Option (3)): seeing that each middle term is the geometric mean of its neighbours shows that the series is a geometric progression, and A then gives its ratio. The answer given by NTA keeps A and B together and puts D last as the property the completed series satisfies, which is why Option (4) is marked.