To determine the common difference in the given sequence [tex]\(9, 2.5, -4, -10.5, -17, \ldots\)[/tex], we need to find the differences between successive terms and observe if these differences are consistent.
Let's begin by calculating each difference step-by-step:
1. Calculate the difference between the second term ([tex]\(2.5\)[/tex]) and the first term ([tex]\(9\)[/tex]):
[tex]\[
2.5 - 9 = -6.5
\][/tex]
2. Calculate the difference between the third term ([tex]\(-4\)[/tex]) and the second term ([tex]\(2.5\)[/tex]):
[tex]\[
-4 - 2.5 = -6.5
\][/tex]
3. Calculate the difference between the fourth term ([tex]\(-10.5\)[/tex]) and the third term ([tex]\(-4\)[/tex]):
[tex]\[
-10.5 - (-4) = -10.5 + 4 = -6.5
\][/tex]
4. Calculate the difference between the fifth term ([tex]\(-17\)[/tex]) and the fourth term ([tex]\(-10.5\)[/tex]):
[tex]\[
-17 - (-10.5) = -17 + 10.5 = -6.5
\][/tex]
After calculating these differences, we observe that each difference is [tex]\(-6.5\)[/tex]. Hence, the common difference between successive terms in the sequence is:
[tex]\[
\boxed{-6.5}
\][/tex]
