Question

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

Explanation:

Step1: Check for common difference (arithmetic sequence)

To find the common difference, subtract consecutive terms.
First, \(-4.8 - 2.4 = -7.2\)
Second, \(9.6 - (-4.8) = 14.4\)
The differences are not the same, so it's not an arithmetic sequence. So options with common difference are incorrect.

Step2: Check for common ratio (geometric sequence)

To find the common ratio, divide consecutive terms.
First, \(\frac{-4.8}{2.4} = -2\)
Second, \(\frac{9.6}{-4.8} = -2\)
Third, \(\frac{-19.2}{9.6} = -2\)
The ratio is consistent (\(-2.0\)).

Answer:

The common ratio is \(-2.0\) (the third option: The common ratio is \(-2.0\))