a. \( 20,10, \ldots, 2.5 \), b. Common difference or ratio? c. Common difference or ratio = d. Arithmetic or geometric?

To analyze the sequence \( 20, 10, \ldots, 2.5 \): a. The sequence is \( 20, 10, \ldots, 2.5 \). b. To determine if the sequence has a common difference or a common ratio, we can look at the differences between consecutive terms and the ratios of consecutive terms. - The difference between the first two terms: \[ 10 - 20 = -10 \] - The difference between the second and third terms: \[ 2.5 - 10 = -7.5 \] Since the differences are not constant, there is no common difference. Next, we can check the ratios: - The ratio of the first two terms: \[ \frac{10}{20} = 0.5 \] - The ratio of the second and third terms: \[ \frac{2.5}{10} = 0.25 \] Since the ratios are not constant, there is no common ratio. c. Since there is no common difference or common ratio, we cannot assign a value for either. d. The sequence is neither arithmetic (which would require a constant difference) nor geometric (which would require a constant ratio). In conclusion: - The sequence does not have a common difference or ratio. - It is neither arithmetic nor geometric.