Question

which best describes the relationship between the successive terms in the sequence shown?
2.4, -4.8, 9.6, -19.2
the common ratio is -2.0. the common difference is -2.4.
the common ratio is -0.5. the common difference is -7.2.

Explanation:

Step1: Check for common ratio (geometric sequence)

To find the common ratio \( r \), divide a term by its previous term.
First, \( \frac{-4.8}{2.4} = -2.0 \)
Second, \( \frac{9.6}{-4.8} = -2.0 \)
Third, \( \frac{-19.2}{9.6} = -2.0 \)

Step2: Check for common difference (arithmetic sequence)

To find the common difference \( d \), subtract a term from its next term.
First, \( -4.8 - 2.4 = -7.2 \)
Second, \( 9.6 - (-4.8) = 14.4 \) (not equal to -7.2), so no common difference.

Answer:

The common ratio is \(-2.0\).