Let's determine whether the sequence $15, 10, 5$ is arithmetic or geometric.

1. Check if the sequence is arithmetic:

• In an arithmetic sequence, the difference between consecutive terms is constant.

• Subtract the second term from the first: $10 - 15 = -5$

• Subtract the third term from the second: $5 - 10 = -5$

• Since the difference is the same, the sequence is arithmetic.

• The common difference ($d$) is $-5$.

2. Check if the sequence is geometric:

• In a geometric sequence, the ratio between consecutive terms is constant.
• Divide the second term by the first: $\frac{10}{15} = \frac{2}{3}$
• Divide the third term by the second: $\frac{5}{10} = \frac{1}{2}$
• Since the ratios are different, the sequence is not geometric.

Conclusion:

• The sequence $15, 10, 5$ is arithmetic, with a common difference of $-5$.

Would you like more details on this, or do you have any questions?

Here are some related questions you might want to explore:

1. What are the formulas for the nth term of an arithmetic sequence?
2. How can you determine the sum of the first n terms of an arithmetic sequence?
3. How would this sequence look if it were geometric instead?
4. Can a sequence be both arithmetic and geometric?
5. What is the graphical representation of an arithmetic sequence?

Tip: For arithmetic sequences, the nth term can be calculated using the formula $a_n = a_1 + (n-1) \cdot d$.