What will be the next number in the series?
$$3,6,18,72,360,\dots$$

Let's find the multiplying factor between consecutive terms of the given number series:
* $3\times 2=6$
* $6\times 3=18$
* $18\times 4=72$
* $72\times 5=360$

The multiplication factor increases by $1$ at each successive step ($\times 2,\times 3,\times 4,\times 5$).
Therefore, to find the next term, we must multiply the last term by $6$:

$$\text{Next number}=360\times 6=2160$$