# Thread: The nth term that is killing me

1. ## The nth term that is killing me

So basically I've got this set of numbers and I've found the pattern but i can't figure out how to into a formula. It's kinda important because it's part of my coursework, which really needs to be posted in the next few days.

So here be the numbers

3,12,30,60,105,168,252
1st set of differences:
9,18,30,45,63,84
2end set of differences:
9,12,15,18,21,24
3erd set of differences:
3,3,3,3,3

I think it's something to do with n^3 but I really can't figure it out.

2. Originally Posted by Salsa
So basically I've got this set of numbers and I've found the pattern but i can't figure out how to into a formula. It's kinda important because it's part of my coursework, which really needs to be posted in the next few days.

So here be the numbers

3,12,30,60,105,168,252
1st set of differences:
9,18,30,45,63,84
2end set of differences:
9,12,15,18,21,24
3erd set of differences:
3,3,3,3,3

I think it's something to do with n^3 but I really can't figure it out.

You can fit the numbers to a cubic model:

$\displaystyle t_n = \frac{n^3}{2} + \frac{3n^2}{2} + n$.

Of course higher degree models also work, so the simple fact is that there's no unique formula.

(But no doubt the person who set this question will be expecting the above cubic formula).

3. Originally Posted by Salsa
So basically I've got this set of numbers and I've found the pattern but i can't figure out how to into a formula. It's kinda important because it's part of my coursework, which really needs to be posted in the next few days.

So here be the numbers

3,12,30,60,105,168,252
1st set of differences:
9,18,30,45,63,84
2end set of differences:
9,12,15,18,21,24
3erd set of differences:
3,3,3,3,3

I think it's something to do with n^3 but I really can't figure it out.

You know:

$\displaystyle t_n=an^3+bn^2+cn+d$

And:

$\displaystyle t_1 = 3$

$\displaystyle t_2 = 12$

$\displaystyle t_3 = 30$

$\displaystyle t_4 = 60$

Can you now use simultaneous equations to find a, b, c, and d?