Final answer:
The common difference of the arithmetic sequence 15/8, 19/8, 23/8, 27/8, 31/8 is 1/2, as each term is increased by 1/2 from the previous term.
Step-by-step explanation:
The sequence provided is an arithmetic sequence, where each term after the first is derived by adding a common difference to the preceding term. In this case, the sequence is 15/8, 19/8, 23/8, 27/8, 31/8. To find the common difference, we only need to subtract any term from the term that follows it.
For example:
- 19/8 - 15/8 = 4/8
- 23/8 - 19/8 = 4/8
- 27/8 - 23/8 = 4/8
All of these differences are equal to 4/8, which simplifies to 1/2. Therefore, the common difference of this arithmetic sequence is 1/2. This value is constant throughout the sequence, which confirms its arithmetic progression nature. By identifying the common difference, we can generate any term in the sequence, predict future terms, and analyze the sequence's behavior as it extends to infinity.