Any number that you choose can be the nth number. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question, and the nth is the number of your choice. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest rule, based on a polynomial of order 4 is
t(n) = (169*n^4 - 1950*n^3 + 7799*n^2 - 12402*n - 6792)/24 for n = 1, 2, 3, ...
If you mean: 6 12 18 24 then the nth term is 6n
The nth term of that series is (24 - 6n).
The sequence has a difference of 10, so the nth term starts with 10n. Then to get to -8 from 10 you need to subtract 18. So the nth term is 10n - 18.
The nth term is 18 -3n and so the next term will be 3
24 - 6n
For {12, 15, 18} each term is the previous term plus 3; a general formula for the nth term is given by t(n) = 3n + 9. For {12, 24, 36} each term is the previous term plus 12; a general formula for the nth term is given by t(n) = 12n.
18 - 6n
The nth term of the sequence is (n + 1)2 + 2.
The nth term in this arithmetic sequence is an=26+(n-1)(-8).
Un = 5n - 2
The nth term is: n^2 +2 and so the next number will be 38
72/2n