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Re: how do i find the nth term?
Posted:
Jan 20, 2004 1:08 PM


> 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



