# Math Help - nth term

1. ## nth term

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.

2. This site can be very useful with this sort of problem.
The On-Line Encyclopedia of Integer Sequences

3. Thanks!

How on earth did I miss the first one is (n!)^2 ?!

But nothing came up for the second sequence, which was a bit odd.

Any ideas?

4. Hello, WWTL@WHL!

The second one is baffling . . .

Find the nth term of: .3, 9, 18, 30, 48, 66, 87, . . .

We have: .3(1), 3(3), 3(6), 3(10), 3(16), 3(22), 2(29) , . . .

We seem to have: 3 times a Triangular Number: . $3 \times \frac{n(n+1)}{2}$
. . but the fifth term breaks the pattern.

The 5th, 6th and 7th terms seem to be: .3 × (a Triangular Number plus 1)

. . So what's going on?

5. Sorry, the sequence should be:

3, 9, 18, 30, 45, 63, .........

I calculated it wrong, and you are right Soroban.

Thank you very much!