Question

determine whether the sequence is arithmetic, geometric or neither.

(0.3, -3, 30, -300, 3000 \dots)

if the sequence is geometric, what is the common ratio?

Explanation:

Step1: Identify consecutive terms

The given sequence is \(0.3, -3, 30, -300, 3000, \dots\).

Step2: Calculate consecutive ratios

Calculate the ratio of consecutive terms:

$$\frac{-3}{0.3} = -10$$

$$\frac{30}{-3} = -10$$

$$\frac{-300}{30} = -10$$

$$\frac{3000}{-300} = -10$$

Step3: Determine sequence type

Since the ratio is constant, the sequence is geometric with a common ratio of \(-10\).

Answer:

The sequence is geometric.
The common ratio is -10.