[apocadam]

Exactly, it's completely arbitrary. I like to frame it in terms of fitting n points (the existing data in the problem) to a polynomial of degree n+1, where there's an infinite number of ways to pick a solution and still satisfy the initial data.

[kaba0]

Maybe the "solution with the lowest Kolmogorov complexity".

In a sibling comment, I replied that usually a repeating pattern can also be applied, but that one usually requires storing the n-sequence, rarely making it the shortest encodable rule.