I found two ways to solve this. The simpler solution is to add 1/12 to each number in the sequence.
1/12 + 1/12 = 2/12 = 1/6
1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4
1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3
For the next number in the sequence:
1/3 + 1/12 = 4/12 + 1/12 = 5/12
Leaving the fractions as 12ths, we have:
1/12 2/12 3/12 4/12 and the new one 5/12