What is the member in the last set of this pattern?

Question

(42,15,3)

(24,20,2)

(?,12,4)

? indicates the number I do not know

Answer 1

One possible answer:

The first term is greater than the second term by the third term raised to itself. Using a formula, the tuples are generated by $$(x+y^y,x,y)$$ for some given $x$ and $y$. It is easy to check that the two given tuples follow this rule. That would make the third tuple $$(12+4^4,12,4)$$ or $?=268$.

Note that this is not the only possible answer, but it does work and is at least somewhat satisfying in my opinion.