Any number can be the next 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 next is the given number. 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 polynomial solution, using a polynomial of order 4, is
t(n) = (3*n^4 - 34*n^3 + 117*n^2 - 62*n + 48)/2 for n = 1, 2, 3, ...
Accordingly, n(6) = 18.
12
11
The next figure would be 21, followed by 11 & 10.
12
The number 7 comes next.
To find the next number in the series 12, 5, 11, 21, we can look at the pattern of differences between the numbers. The differences are: -7 (12 to 5), +6 (5 to 11), and +10 (11 to 21). Continuing this pattern, we can assume the next difference will be +6 (to alternate between decreasing and increasing). Therefore, the next number would be 21 + 6 = 27.
12
12
8, 11, 12, 15...............
10
11
11.