Final answer:
The given sequence is geometric with a common ratio of 3. The next term in the sequence is 486.
Step-by-step explanation:
The given sequence is 6, 18, 54, 162, and so on. To determine if the sequence is arithmetic or geometric, we need to check if there is a common difference between consecutive terms or a common ratio. Let's calculate the differences or ratios between the terms:
18/6 = 3, 54/18 = 3, 162/54 = 3, ...
Since the ratios are all equal to 3, the sequence is geometric and the common ratio is 3.
Therefore, the next term in the sequence is:
162 * 3 = 486