What number should come next in the sequence 6, 18, 72, 360, 2160______?

Let us determine the operational pattern regulating the progression of numbers in the sequence:
* $6\times 3=18$
* $18\times 4=72$
* $72\times 5=360$
* $360\times 6=2160$

The sequence expands by multiplying each subsequent number by a value that increases by $1$ at each step ($3,4,5,6$). Therefore, to find the next term, we must multiply the last term by $7$:

$$\text{Next number}=2160\times 7=15120$$