Final answer:
The sequence has a pattern where numerators double and then decrease by one, and denominators double with the doubling sequence increasing exponentially.
Step-by-step explanation:
The student has asked to identify the pattern in the sequence 5/1, 10/2, 9/2, 18/4, 17/8, 34/32, 33/256...
Upon analyzing the sequence, we can observe two alternating patterns for the numerators and denominators. For the numerators: they start at 5, and with each step, they double and then decrease by one (e.g., 5 becomes 10 when doubled, minus 1 gives 9, which becomes 18 when doubled, minus 1 gives 17, and so on). For the denominators: they also start at 1 with each step they double, and then the doubling sequence itself doubles (e.g., 1 becomes 2, next double is 4, next is 8, but then it skips to 32, which is four times the previous double of 8, then to 256, which is eight times the previous double of 32).
The pattern involves both doubling the previous term's numerator and an exponential increase in the denominator's doubling factor.