what is the common difference between successive terms in the sequence? 9, 2.5, -4, -10.5, -17…

Explanation:

Step1: Recall common - difference formula

The common difference $d$ of an arithmetic sequence is $d=a_{n + 1}-a_{n}$, where $a_{n+1}$ is the $(n + 1)$ - th term and $a_{n}$ is the $n$ - th term.

Step2: Select two consecutive terms

Let's take the first two terms $a_1 = 9$ and $a_2=2.5$.

Step3: Calculate the common difference

$d=a_{2}-a_{1}=2.5 - 9=-6.5$. We can double - check with other consecutive terms. For example, if we take $a_3=-4$ and $a_2 = 2.5$, then $d=a_{3}-a_{2}=-4 - 2.5=-6.5$.

Answer:

B. -6.5