Which of the following is an arithmetic sequence?

Explanation

To determine which sequence is an arithmetic sequence, we first need to understand what an arithmetic sequence is. An arithmetic sequence is a list of numbers where the difference between consecutive terms is always the same, known as the common difference. Let’s analyze each option: A. 2, 4, 16, 32 Differences: 4 - 2 = 2, 16 - 4 = 12, 32 - 16 = 16 This does not have a consistent difference, so it is not an arithmetic sequence. B. 2, 3, 7, 1 Differences: 3 - 2 = 1, 7 - 3 = 4, 1 - 7 = -6 Here the differences are not the same, hence it is not an arithmetic sequence. C. 3, 0, -3, -6 Differences: 0 - 3 = -3, -3 - 0 = -3, -6 - (-3) = -3 The common difference is consistent at -3, therefore this is an arithmetic sequence. D. 5, -5, 5, -5 Differences: -5 - 5 = -10, 5 - (-5) = 10, -5 - 5 = -10 The differences alternate between -10 and 10, so it is not an arithmetic sequence. Based on this analysis, option C: 3, 0, -3, -6 is the only arithmetic sequence due to its consistent common difference of -3.