To determine the common difference of an arithmetic sequence, we need to find the difference between successive terms.
Let's look at the given sequence:
[tex]\[
-18, -22.5, -27, -31.5, -36
\][/tex]
By definition, the common difference [tex]\( d \)[/tex] in an arithmetic sequence is the difference between any two consecutive terms. We'll find this difference by subtracting the first term from the second term:
[tex]\[
d = -22.5 - (-18)
\][/tex]
Solving inside the parentheses first:
[tex]\[
-22.5 - (-18) = -22.5 + 18
\][/tex]
Carrying out the subtraction:
[tex]\[
-22.5 + 18 = -4.5
\][/tex]
So, the common difference between the elements of the sequence is:
[tex]\[
\boxed{-4.5}
\][/tex]
To verify, let's check the difference between another pair of successive terms:
Between the second and third terms:
[tex]\[
d = -27 - (-22.5) = -27 + 22.5 = -4.5
\][/tex]
Between the third and fourth terms:
[tex]\[
d = -31.5 - (-27) = -31.5 + 27 = -4.5
\][/tex]
Between the fourth and fifth terms:
[tex]\[
d = -36 - (-31.5) = -36 + 31.5 = -4.5
\][/tex]
Since the difference is consistent, our common difference is confirmed to be:
[tex]\[
\boxed{-4.5}
\][/tex]
