Question

which best describes the relationship between the successive terms in the sequence show 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 \(d\), we subtract consecutive terms.
First, \( -1 - 9 = -10 \)
Second, \( -11 - (-1) = -11 + 1 = -10 \)
Third, \( -21 - (-11) = -21 + 11 = -10 \)

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

To find the common ratio \(r\), we divide consecutive terms.
First, \( \frac{-1}{9} \approx -0.11 \)
Second, \( \frac{-11}{-1} = 11 \)
Third, \( \frac{-21}{-11} \approx 1.91 \)
Since the ratio is not constant, it's not a geometric sequence. Since the difference is constant (\(-10\)), it's an arithmetic sequence with common difference \(-10\).

Answer:

The common difference is \(-10\).