Write the next term of each of the following sequences :
$0,2,6,12,20,.....$

We observe that,

From the first difference, its easy to notice that that the next difference will be 12, which makes the next term to be 30.

Putting $n=1,2,3$

Solving these, we get

So, putting $n=6$

Next term$=30$

So, the series is

0,2,6,12,30,42..............so on.