What is the nth term of 10 13 18 25 34?

Answer 1

According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid.
The simplest quadratic function, in this case, is U(9) = n^2 + 9 for n = 1, 2, 3, ...