Nth terms' pattern pattern

[CT0581]

Hey!
So, I kinda need some help...
I'm trying to work out the nth term of this, but it's beginning to get hard, I remember when it goes into the nth term term you need to square things, and stuff...

2)  100,000
           - 200,000
3)  300,000         - 100,000 
           - 300,000
4)  600,000         - 100,000
           - 400,000
5)1,000,000


			2) 50,000
			3)100,000
			4)150,000
			5)200,000
			50(n-1)

2) 50,000
3)200,000
4)450,000
5)800,000

-
That was just my rough working out, if you can understand any of it, a head-start. Otherwise, my pattern is

2)  100,000
3)  300,000
4)  600,000
5)1,000,000

I've forgotten how to do this, and all of the online sites are useless!
Thanks if anyone helps.

[CT0581]

I think I may have found it.
10,000(10(n-1)) + 50(n-1)
I'm testing it now, but I think.


----


I got it!! It's:
(10000 * (10 * ($n-1)) + 50000 * ($n-1)) / 3 * 2 * ($n / 2)

[CT0581]

But of course you know that was using the old trial and error. I have about 30 of these to do, and trial and erro does not apply onto ones like this

2) 4,800
3)12,000
4)21,600
5)33,600

...Can someone tell me the actual way to do this please?

[NotLKH]

This might help you out:

BTW, in Step2, AX0 represents B from the Difference Pyramid.

[NotLKH]

But of course you know that was using the old trial and error. I have about 30 of these to do, and trial and erro does not apply onto ones like this

2) 4,800
3)12,000
4)21,600
5)33,600

...Can someone tell me the actual way to do this please?

So:

Lets build a difference tree:

4800 12000 21600 33600
7200 9600 12000
2400 2400

So, as you see, the elements of a line below another line is equal to the above right number minus the above number.

And as you see, the last line contains identical elements.

So, the equation becomes:

Y = 4800 + 7200*X + 2400*X(X-1)/2
==> 4800 + 7200*X + 1200*X² - 1200*X
==> 4800 + 6000*X + 1200*X²

Or:

Y = 1200*(X² + 5*X + 4)

So, when X=0,1,2,3...:

X Y
0 4800
1 12000
2 21600
3 33600
and so on

-Lou