To determine the common difference between consecutive terms in the given arithmetic sequence [tex]\(-11, -8, -5, -2, 1, \ldots\)[/tex], we need to analyze the differences between each pair of consecutive terms.
An arithmetic sequence has a constant difference, called the common difference, between each pair of consecutive terms. Let's find this common difference step-by-step:
1. Identify the sequence terms:
[tex]\[
-11, -8, -5, -2, 1, \ldots
\][/tex]
2. Calculate the difference between the first and second terms:
[tex]\[
-8 - (-11) = -8 + 11 = 3
\][/tex]
3. Calculate the difference between the second and third terms:
[tex]\[
-5 - (-8) = -5 + 8 = 3
\][/tex]
4. Calculate the difference between the third and fourth terms:
[tex]\[
-2 - (-5) = -2 + 5 = 3
\][/tex]
5. Calculate the difference between the fourth and fifth terms:
[tex]\[
1 - (-2) = 1 + 2 = 3
\][/tex]
We can observe that the difference between each pair of consecutive terms is consistently 3. Hence, the common difference for the given arithmetic sequence is:
[tex]\[
\boxed{3}
\][/tex]
