This is something I should have learned in high school, but I never quite got it.

Write down explicit formulate for the following sequences:

1, 4, 36, 576, 14400, 518400 ...........

For this, I squared rooted the numbers.. so I'm trying to find the pattern between:

1, 2, 6, 24, 120, ...... but I can't find it. Is there a systematic approach to find the nth term for such a sequence? Obviously the arithmetic and geometric formulas won't work. But is there another logical way?

And secondly, find the nth term of:

3, 9, 18, 30, 48, 66, 87 ..........

Now, again, I can see some sort of pattern. 9-3 = 6, 18-9 = 9, 30-18 = 12, =15, =18 etc. But I can't apply this.

Please help. Thanks.