Question

which best describes the relationship between the successive terms in the sequence shown?
9, -1, -11, -21, ...

the common difference is -10.
the common difference is 10.
the common ratio is -9.
the common ratio is 9.

Explanation:

Step1: Check if it's an arithmetic sequence (common difference)

To find the common difference, subtract consecutive terms.
First, $-1 - 9 = -10$.
Second, $-11 - (-1) = -11 + 1 = -10$.
Third, $-21 - (-11) = -21 + 11 = -10$.
So the common difference is $-10$.

Step2: Check if it's a geometric sequence (common ratio)

To find the common ratio, divide consecutive terms.
First, $\frac{-1}{9} \approx -0.11$, which is not equal to $\frac{-11}{-1} = 11$, so it's not a geometric sequence. Thus, common ratio options are invalid.

Answer:

The common difference is $-10$. (The option: The common difference is $-10$)