Write a possible explicit rule for {-7,-6,-5,-4,-3...}

A possible explicit rule for the sequence \(-7, -6, -5, -4, -3, \dots\) can be given by the formula:

\[
a_n = -8 + n
\]

where \(a_n\) represents the \(n\)-th term of the sequence.

### Explanation:

- The sequence starts at \(-7\), and the difference between consecutive terms is \(1\).
- When \(n = 1\), \(a_1 = -8 + 1 = -7\).
- As \(n\) increases by 1, the value of \(a_n\) increases by 1 as well.

Would you like details or have any questions?

Here are 8 related questions:
1. How would you find the \(n\)-th term of the sequence \(3, 5, 7, 9, \dots\)?
2. Can you derive a formula for the sum of the first \(n\) terms of an arithmetic sequence?
3. What is the general form of an arithmetic sequence?
4. How do you find the common difference in an arithmetic sequence?
5. What would be the 20th term in the sequence \(-7, -6, -5, -4, \dots\)?
6. How does the explicit rule change if the sequence starts at a different number, like \(-10\)?
7. Can you describe how to convert an arithmetic sequence into a recursive formula?
8. What are the conditions for a sequence to be arithmetic?

**Tip:** In arithmetic sequences, the difference between any two consecutive terms is constant, which is known as the "common difference."

Learn how to find the explicit rule for the sequence -7, -6, -5, -4, -3 with a detailed explanation. This problem covers arithmetic sequences, including the formula a_n = -8 + n. Suitable for students in Grades 7-9.

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