A column of fractions: 3 out of 20, 5 out of 34, 8 out of 55, 12 out of 83. What's the next, the nth

A column of fractions: 3 out of 20, 5 out of 34, 8 out of 55, 12 out of 83. What's the next, the nth

The law of numerator and denominator in this column is separate, so you need to find the law of numerator (denominator) separately
For example, molecules: 2, 3 (2 + 1), 5 (3 + 2), 8 (5 + 3), 12 (8 + 4)
For example, denominators: 13, 20 (13 + 7 × 1), 34 (13 + 7 × 2), 55 (34 + 7 × 3), 83 (55 + 7 × 4)
As for the N, I don't know. The only thing I can do is this. If you like, you can try by yourself and see if you can guess