Final answer:
Of the given sequences, the sequences 4, 1, -2, -5, -8, ... and 1.0, 1.2, 1.4, 1.6, ... are considered arithmetic because they have constant differences between consecutive terms. The sequence 9, -10, 11, -12, ... is not arithmetic as it lacks a constant difference.
Step-by-step explanation:
To determine which of the following sequences are arithmetic, we need to check if there is a common difference between consecutive terms. An arithmetic sequence has a constant difference (common difference) between any two successive terms.
- For the sequence 4, 1, -2, -5, -8, ... we subtract the second term from the first, the third from the second, and so on: 1 - 4 = -3, -2 - 1 = -3, -5 - (-2) = -3, ... Since the difference is constant at -3, this sequence is arithmetic.
- The sequence 9, -10, 11, -12, ... does not have a constant difference: -10 - 9 = -19, 11 - (-10) = 21, ... Since the differences are not the same, this is not an arithmetic sequence.
- For the sequence 1.0, 1.2, 1.4, 1.6, ... the differences are: 1.2 - 1.0 = 0.2, 1.4 - 1.2 = 0.2, 1.6 - 1.4 = 0.2, ... All differences are constant at 0.2, so this sequence is also arithmetic.
Therefore, the sequences 4, 1, -2, -5, -8, ... and 1.0, 1.2, 1.4, 1.6, ... are arithmetic.