Find the common difference of the arithmetic sequence minus, 11, comma, minus, 17, comma, minus, 23, comma, point, point, .−11,−17,−23,...

To find the common difference of an arithmetic sequence, we use the formula for the common difference \(d\) between two consecutive terms:

\[
d = a_{n+1} - a_n
\]

Let’s apply this to the first two terms of the sequence:

- The first term \(a_1 = -11\)
- The second term \(a_2 = -17\)

The common difference between the first and second terms is:

\[
d = a_2 - a_1 = -17 - (-11) = -17 + 11 = -6
\]

To verify, we can check the difference using the second and third terms:

- The second term \(a_2 = -17\)
- The third term \(a_3 = -23\)

The common difference between the second and third terms is:

\[
d = a_3 - a_2 = -23 - (-17) = -23 + 17 = -6
\]

Since the common difference is consistent between the terms, the common difference of the arithmetic sequence is \(-6\).

Would you like further details or do you have any questions? Here are some related questions you might find interesting:

1. How do you find the nth term of an arithmetic sequence?
2. What is the sum of the first \(n\) terms of an arithmetic sequence?
3. Can the common difference in an arithmetic sequence be a fraction?
4. What is the difference between arithmetic and geometric sequences?
5. How do you determine if a sequence is arithmetic?
6. What happens to the terms of an arithmetic sequence if the common difference is zero?
7. How can arithmetic sequences be applied in real-life situations?
8. How do you find the average of the first and last terms of an arithmetic sequence?

**Tip:** Always verify the common difference using more than one pair of terms to ensure the sequence’s consistency.

Learn how to find the common difference of the arithmetic sequence -11, -17, -23 with a step-by-step solution. Understand the concept of arithmetic sequences and how to calculate the common difference between consecutive terms. Suitable for students in Grades 7-9.

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