Question

What is the common difference between successive terms in the sequence?

9, 2.5, –4, –10.5, –17, ...

–11.5
–6.5
6.5
11.5

Answer 1

(a term) - (term before) = (difference)

Answer 2

So if we use the following notations,
\(a_n\) - some Nth term.
\(a_{n+1}\) - some term which is right after the Nth term.
\(d\) - common differnce

Then, the "difference" is by definition,
\(a_{n+1}-a_n=d\)

Answer 3

(a_n=a_1+(n-1)d
a_2 implies 2.5=9+(1)d 2.5-9=d
-6.5=d

Answer 4

However,
\(a_{n+1}-a_n=d\)
Has to give you the same difference for all n, and if that is not the case, then your sequence is not an arithmetic sequence (if is a sequence at all), and no common difference is going to exist.

(How can there be a common differnce if the difference varies?)