Question

what is the common difference between successive terms in the sequence?
9, 2.5, -4, -10.5, -17, ...
-6.5
11.5
-11.5
6.5

Explanation:

Step1: Recall the formula for common difference

The common difference \(d\) between successive terms in an arithmetic sequence is given by \(d = a_{n + 1}-a_{n}\), where \(a_{n+1}\) is the next term and \(a_{n}\) is the current term.

Step2: Calculate the difference between the second and first term

Take the first two terms: \(a_1 = 9\) and \(a_2=2.5\). Then \(d=a_2 - a_1=2.5 - 9=- 6.5\).

Step3: Verify with other terms (optional but good for confirmation)

Check with the second and third term: \(a_2 = 2.5\), \(a_3=-4\). Then \(d=-4 - 2.5=-6.5\).
Check with the third and fourth term: \(a_3=-4\), \(a_4 = - 10.5\). Then \(d=-10.5-(-4)=-10.5 + 4=-6.5\).
Check with the fourth and fifth term: \(a_4=-10.5\), \(a_5=-17\). Then \(d=-17-(-10.5)=-17 + 10.5=-6.5\).

Answer:

\(-6.5\) (corresponding to the option: \(-6.5\))