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**Joseph****Guest**

Todays homework included this number sequence that I can`t figure out. Can someone help?

$1, $5, ___, $20, ___, $100

**pi man****Member**- Registered: 2006-07-06
- Posts: 251

How about $10 and $50. That would be all of the US bill denominations in ascending order.

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

There is a very extreme method, you can assume a function with four unknown coefficients, and replace the number given above to determine all coefficients.

Like F(x)=aX^3+bX^2+cX+d, then when x=1, f(1)=1.

x=2 , f(2)=5 , x=4, f(4)=20, x=6, f(6)=100

Numbers are the essence of the Universe

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

pi man wrote:

How about $10 and $50. That would be all of the US bill denominations in ascending order.

I guess this is the most logical solution.

Of course, we can always see the sequence as data points and try interpolation methods and other complex stuff. But the simplest solution seems to fit in ; )

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**Joseph****Guest**

Thanks for all your help everybody!

**numen****Member**- Registered: 2006-05-03
- Posts: 115

x is the position of the number in the sequence. Check it for f(1), f(2), f(4) and f(6) in the sequence, it's correct It doesn't give integers for f(3) and f(5) though. Stanley_Marsh made me want to try it out heh.

Bang postponed. Not big enough. Reboot.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Hehe, very good. I tried to get Excel to do it, but it gave me the result in rounded decimal form, and I didn't want to try to decipher it.

I'm trying to work out the sequence by the method of differences now, and I've realised that you can actually work out what the missing terms would be much easier than it would be to work out the nth term.

Labelling f(3) as x and f(5) as y, you can take differences and discover that the following three expressions must all be equal (assuming I've got my maths right):

-3x+36

3x+y-65

-x-2y+160

By equating these and doing some cancelling and rearranging, you can work out what x and y would be. In fact, in this method you *have* to do that in order to continue.

How did you work it out, numen?

Why did the vector cross the road?

It wanted to be normal.

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