Final answer:
The missing terms in the arithmetic sequence are 2/3 and 4/3, with a common difference of 2/3. Thus, the correct option is B) 1, 5/3, 7/3, 2, 8/3; common difference: 2/3.
Step-by-step explanation:
To find the missing terms in the arithmetic sequence, we must first determine the common difference. An arithmetic sequence is characterized by the same difference between consecutive terms. This sequence starts with 0, and we are given later terms 2 and 8/3. We can use these terms to find the common difference:
The difference between 2 and 8/3 is 8/3 - 2 = 8/3 - 6/3 = 2/3. Since the common difference must be consistent across the sequence, we can subtract the same amount, 2/3, from 2 to find the term before it.
2 - 2/3 = 6/3 - 2/3 = 4/3. Again, subtract 2/3 from 4/3 to find the first missing term:
4/3 - 2/3 = 4/3 - 2/3 = 2/3. Therefore, the sequence fills in as follows:
Thus, the missing terms are 2/3 and 4/3, with a common difference of 2/3. So, the correct answer is B) 1, 5/3, 7/3, 2, 8/3; common difference: 2/3.