To determine whether the sequence $\{2, 4, 6, \dots\}$ is geometric, we need to check if the ratio between consecutive terms is constant. This ratio is called the common ratio (r) in a geometric sequence.

Steps:

1. Find the ratio between consecutive terms:

   • The first term is 2, the second term is 4, and the third term is 6.

   The ratio between the second term and the first term: $r = \frac{4}{2} = 2$

   The ratio between the third term and the second term: $r = \frac{6}{4} = 1.5$

2. Check if the ratio is constant:

   • The ratios between consecutive terms are not equal (2 and 1.5). Hence, the ratio is not constant.

Conclusion:

Since the ratio between consecutive terms is not the same, the sequence $\{2, 4, 6, \dots\}$ is not geometric.

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Would you like to go over how to determine geometric sequences in more detail? Here are some related questions you might find helpful:

1. How do you find the common ratio in a geometric sequence?
2. What is the general formula for the $n$-th term of a geometric sequence?
3. How can you identify a geometric sequence from a formula?
4. What is the difference between arithmetic and geometric sequences?
5. Can a sequence with a negative common ratio still be geometric?

Tip: For geometric sequences, always check if the ratio of consecutive terms is constant. If it is, the sequence is geometric!