To figure out if a list of numbers is a geometric sequence, look for a pattern in how each number relates to the one before it. In a geometric sequence, you get each term by multiplying the last term by a certain number called the common ratio.

Here’s how to check:

1. Calculate Ratios: Take two numbers that are next to each other (consecutive terms). Divide the second number by the first one. Do this for all pairs of numbers.

   For example, let’s look at this sequence: 2, 6, 18, 54.

   • For the second term (6) and the first term (2): $\frac{6}{2} = 3$
   • For the third term (18) and the second term (6): $\frac{18}{6} = 3$
   • For the fourth term (54) and the third term (18): $\frac{54}{18} = 3$

   Since the ratio is always 3, this means it is a geometric sequence.

2. Common Ratio: If all the ratios are the same, that number is your common ratio ($r$). In our example, $r = 3$.

3. Finding the nth Term: You can find any term in the sequence using this formula:

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

   Here, $a_1$ is the first term. For our sequence, the formula would look like this:

   $a_n = 2 \cdot 3^{(n-1)}$

By following these simple steps, you can easily find geometric sequences in any list of numbers!