Question

Using the following pattern determine the number in the 4th place:
9, 12, 18, .....

Answer 1

12-9 ≠ 18-12 , so not arithmetic
12/9 ≠ 18/12 , so not geometric

9 = 3x3
12 = 3x4
18 = 3x6
almost a pattern, would have been nice had the terms been 9, 12, 15, 18

I see no apparent pattern, perhaps somebody else can see something.

Answer 2

Of course, there are infinitely many solutions, but if you want a polynomial,

3/2 (x^2 - x + 6) is the lowest-degree one which generates the given data.