Final answer:
The common difference of the given sequence is -1/4; it is found by subtracting each term from the subsequent term and noting that the difference is consistent across all consecutive pairs of terms.
Step-by-step explanation:
To find the common difference of the given sequence 9, 35/4, 17/2, 33/4, 8, 31/4, we need to subtract each term from the following term. Let's calculate the differences step by step:
- (35/4) - 9 = (35/4) - (36/4) = -1/4
- (17/2) - (35/4) = (34/4) - (35/4) = -1/4
- (33/4) - (17/2) = (33/4) - (34/4) = -1/4
- 8 - (33/4) = (32/4) - (33/4) = -1/4
- (31/4) - 8 = (31/4) - (32/4) = -1/4
With each difference being -1/4, we can confirm that the common difference is -1/4.