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Topic: how do i find the nth term?
Replies: 3   Last Post: Jan 20, 2004 1:08 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: how do i find the nth term?
Posted: Jan 20, 2004 1:08 PM
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> On Jan 19, 2004, at 12:39 PM, Laura wrote:
>

> > Im really stuck on this sequence of numbers; 5, 20, 50, 100, 175, 280,
> > and how to find the formula for the nth term. Please can anybody
> > enlighten me?!


If your sequence consists of successive values of an nth degree
polynomial, then its nth differences will be constant. This
happens for the third differences in this example:

5 20 50 100 175 280
15 30 50 75 105
15 20 25 30
5 5 5

and so it's a cubic. The formula, supposing you number the terms
correctly, is found from the leading diagonal, namely:
/n\ /n\ /n\ /n\
5( ) + 15( ) + 15( ) + 5( )
\0/ \1/ \2/ \3/,

where those funny brackets represent binomial coefficients.

John Conway





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