Final answer:
The next three numbers in the sequence after 7/16 are 1/2, 9/16, and 5/8, following the pattern of adding 1/16 each time and simplifying when possible.
Step-by-step explanation:
The sequence provided appears to operate with an increasing pattern in the denominators, in which every odd fraction increases by 1/16 and every even fraction is a simplified form of the odd ones.
Let's continue the sequence one step at a time:
After 7/16, we add 1/16 to get 8/16, which simplifies to 1/2.
Next, we add 1/16 to that to get 9/16, which doesn't simplify, so our next term is 9/16.
Following the pattern, adding another 1/16 brings us to 10/16, which simplifies to 5/8.
Therefore, the next three numbers in the sequence after 7/16 are 1/2, 9/16, and 5/8.