The series follows an alternating addition pattern of adding 1 and then adding 4. Adding 1 to 3 gives 4, adding 4 to 4 gives 8, adding 1 to 8 gives 9, adding 4 to 9 gives 13, and adding 1 to 13 gives 14. Therefore, the next step is to add 4 to 14, which results in 18.