Correct Answer:
B. Exponential growth
Correct Answer: B: Exponential growth
The relationship in the sequence 2, 6, 18, 54 is indeed exponential growth. In an exponential sequence (specifically, a geometric progression), each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In this sequence, if you divide any term by its preceding term, you get 3 (6/2 = 3, 18/6 = 3, 54/18 = 3). This constant multiplier indicates that the numbers are growing at an increasingly rapid rate, which is the hallmark of exponential growth.
The other options are incorrect for the following reasons:
- A: Linear: A linear relationship would involve adding a constant value to each term to get the next one (e.g., 2, 5, 8, 11, where 3 is added each time). This is clearly not the case here, as the difference between terms increases (4, 12, 36).
- C: Decreasing: The sequence is clearly increasing, with each subsequent number being larger than the previous one. A decreasing sequence would show terms getting smaller.
- D: Random: A random sequence would have no discernible pattern or rule governing the progression of its terms. This sequence, however, follows a very clear and consistent pattern of multiplication by 3.