## relatively simple sequence

For the discussion of math. Duh.

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### relatively simple sequence

Can somebody please explain how to derive that the explicit formula for
-1, 5, -9, 13, -17, ...

is a sub n = [(-1)^n](4n-3), n >= 1; or a sub n = [(-1)^(n+1)](4n+1)

I do not understand how it can be done

Dmitry.
Dmitry

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### Re: relatively simple sequence

The only difference there is whether you consider the first element (-1) to be a0 or a1.
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gmalivuk
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### Re: relatively simple sequence

I understand the part of (-1)^n and (-1)^(n+1)

what i do not understand is, what follows that.

why 4n-3, and why 4n+1
Dmitry

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Joined: Mon May 07, 2012 12:44 am UTC

### Re: relatively simple sequence

Taking the absolute value of everything, the series is 1, 5, 9, 13, 17, 21, etc.. If you take the differences between successive elements, you get 4, 4, 4, 4, etc., which tells you that the series can be expressed as 4*0 + 1, 4*1 + 1, 4*2 + 1, etc. An easy way to express this would be an = 4n + 1, having the first element, 1, as a0. If you wanted 1 to be a1 instead, then you would have an = 4(n-1) + 1 = 4n + 1 - 4 = 4n - 3. Afterwards, just add in the (-1)n or (-1)n+1, depending on which way you chose to describe the series.
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### Re: relatively simple sequence

Alright that cleared it up!

Thanks =]
Dmitry

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Joined: Mon May 07, 2012 12:44 am UTC