The sequence provided in the image is: $-4, 9, 15, 18, \dots$.

Let's analyze each part of the question.

1. Is the sequence arithmetic?

To check if the sequence is arithmetic, we need to determine if there is a common difference between consecutive terms.

The differences between consecutive terms are:

• $9 - (-4) = 13$
• $15 - 9 = 6$
• $18 - 15 = 3$

Since the differences between consecutive terms are not constant, the sequence is not arithmetic.

2. Common difference?

Since the sequence is not arithmetic, there is no common difference.

3. $a_7$ (7th term)?

Since the sequence is not arithmetic, there is no reliable formula to determine the 7th term. Hence, the answer would be none.

4. Explicit formula?

As the sequence is not arithmetic, there is no explicit formula based on a common difference. Hence, none.

5. Recursive formula?

Similarly, since the sequence is not arithmetic, there is no recursive formula that can be derived based on a common difference. So, the answer is none.

Would you like a deeper explanation or any clarifications on this?

Here are 5 questions that expand on the above information:

1. How do you determine whether a sequence is arithmetic?
2. What are the steps to find a common difference in a sequence?
3. Can a sequence be classified as neither arithmetic nor geometric? If yes, what type could it be?
4. What is the general form of an explicit formula for an arithmetic sequence?
5. How does a recursive formula work in arithmetic sequences?

Tip: Always check for a constant difference between consecutive terms to identify arithmetic sequences!