An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k.
For letter A. 3,6,12,24,48: you multiply each number by constant k,3.
For letter B. 1,3,6,10,15: you add 2 the first time, 3 the second, 4 the third time, and 5 the last time. This doesnt work because you are adding different numbers everytime.
For letter C. 1,3,5,7,9: This is the correct answer because you add the number 2 everytime
For letter D. 2,4,7,11,16,22: you add 2 th first time, 3 the next time, 4 the next time, 4 the next time, and finally 6 the last time. Similar to letter B, you are adding different numbers each time