Final answer:
Arithmetic sequences (A) 2, 4.5, 7, 9.5, (B) 3, 5.5, 8, 10.5, and (C) 1.5, 4, 6.5, 9 each have a common difference of 2 and 1/2 (or 2.5).
Step-by-step explanation:
To identify which arithmetic sequence has a common difference of 2 and 1/2, or 2.5, we need to examine the difference between consecutive terms in the provided options. Let's calculate the differences for each sequence:
- (A) 2, 4.5, 7, 9.5: The difference between each term is 2.5, which indeed has a common difference of 2.5.
- (B) 3, 5.5, 8, 10.5: The difference between each term is 2.5, which also has the common difference we are looking for.
- (C) 1.5, 4, 6.5, 9: The difference between each term is 2.5, matching our common difference requirement.
- (D) 2, 4, 6, 8: The difference between each term is 2, which does not match our common difference of 2.5.
Upon reviewing the differences between the terms in each option, the sequences in options (A), (B), and (C) all have the common difference of 2.5. Therefore, the arithmetic sequences in options (A), (B), and (C) match the stated condition.