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.