The sequence given is $14, 9, 4, \ldots$.

To determine whether it is arithmetic or geometric, let's analyze the pattern:

1. Arithmetic Sequence Test: An arithmetic sequence has a constant difference between consecutive terms. Calculate the differences: $9 - 14 = -5 \quad \text{and} \quad 4 - 9 = -5$ Since the difference is consistent ($-5$), this is an arithmetic sequence.

2. Common Difference: The common difference is $-5$.

Final Answer:

• This is an arithmetic sequence.
• The common difference is $-5$.

Would you like further clarification or a deeper explanation?

Follow-Up Questions:

1. What is the general formula for the $n$-th term of this sequence?
2. Can you find the 10th term in this sequence?
3. How does an arithmetic sequence differ from a geometric sequence?
4. Can this sequence ever have a positive term after the initial one?
5. How would this change if the common difference were positive?

Tip:

When analyzing sequences, always verify consistency in the differences (arithmetic) or ratios (geometric) across several terms!