You have the following arithmetic sequence:
5, 9, 13, 17
due to the it is an arithmetic sequence, difference between consecutive numbers is constant.
In fact, when you calculate the difference between consecutive numbers you have:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
To determine the next three terms it is necessary to sum 4 (the previous result) to each previous term, just as follow:
17 + 4 = 21
21 + 4 = 25
25 + 4 = 29
Hence, 21, 25 and 29 are the next three terms
