The given sequence is:

6, 18, 54, 162, ...

To determine the pattern, let's examine the relationship between consecutive terms.

1. Calculate the ratio between consecutive terms:
   • $\frac{18}{6} = 3$
   • $\frac{54}{18} = 3$
   • $\frac{162}{54} = 3$

Each term is obtained by multiplying the previous term by 3. This indicates that the sequence is a geometric sequence with a common ratio of 3.

2. General Formula: The general form of a geometric sequence is given by:

   $a_n = a_1 \times r^{(n-1)}$

   Here:

   • $a_1 = 6$ (the first term)
   • $r = 3$ (common ratio)

   Therefore, the $n$-th term of the sequence can be expressed as:

   $a_n = 6 \times 3^{(n-1)}$

3. Next Term Calculation: To find the next term after 162:

   • The current term (162) is the 4th term ($a_4$).
   • The next term ($a_5$) would be:

   $a_5 = 162 \times 3 = 486$

So, the next term in the sequence is 486.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What would be the 10th term of this sequence?
2. How do you find the sum of the first $n$ terms of a geometric sequence?
3. What is the formula for the sum to infinity of a geometric series, and when does it apply?
4. How can you determine if a sequence is geometric or arithmetic?
5. What happens if the common ratio of a geometric sequence is a fraction?

Tip: When identifying the type of sequence, always check the difference or ratio between consecutive terms. For arithmetic sequences, the difference is constant, while for geometric sequences, the ratio is constant.