Consecutive integers are like 1, 2, and 3. They are in a row. Think about plugging numbers in for x. 1 and 1+2 are not consecutive, so A is not the answer. B and C don't start with x, so they aren't the answer. That leaves D, because it starts with x, then goes to x+1, and then to x+2. These are consecutive, because if x was 1, it would be 1, 2, 3.
The given sequence is linear. This means that it is an arithmetic sequence. In an arithmetic sequence, each successive term differ by a common difference. The given set of numbers is
1/4, 5/16, 3/8,....
The second term - the first term = the third term - the second term