To determine the common difference in an arithmetic sequence, we need to subtract each term from the following term and check if the difference remains constant throughout the sequence.
Consider the sequence: [tex]\(9, 2.5, -4, -10.5, -17, \ldots\)[/tex]
1. Calculate the difference between the first and second terms:
[tex]\[ 2.5 - 9 = -6.5 \][/tex]
2. Calculate the difference between the second and third terms:
[tex]\[ -4 - 2.5 = -6.5 \][/tex]
3. Calculate the difference between the third and fourth terms:
[tex]\[ -10.5 - (-4) = -10.5 + 4 = -6.5 \][/tex]
4. Calculate the difference between the fourth and fifth terms:
[tex]\[ -17 - (-10.5) = -17 + 10.5 = -6.5 \][/tex]
We observe that the difference between each pair of successive terms is consistently [tex]\(-6.5\)[/tex]. Therefore, the common difference in the sequence is [tex]\(-6.5\)[/tex].
So, among the given choices, the common difference is:
[tex]\(\boxed{-6.5}\)[/tex]
