Recursive Formula of Quadratic Sequence - HELP PLEASE!

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katyw

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Feb 28, 2006
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Math test tomorrow and I'm doing the review, have realized I have no clue how to do this one type of problem...when given a sequence thats quadratic (as in, the second-order differences are equal), putting it into the recursive formula/rule...

The formula the teacher gave us was kind of vague, I have written down that

Q1 (cant do subscripts, pretend the 1 is small) = first term
Qn = Qn-1 + SODn + c, and that SODn + c has to add up to FOD for any given term

SOD meaning second order difference
FOD meaning first order difference

So...my problem is with finding that "c"...for example, here's the problem I'm stuck on (although its really the concept in general):

Find the recursive formula for the following sequence:

-2, 0, 3, 7, 12 ...

I've gotten as far as

Q1 = -2
Qn = Qn-1 + n + c

but I don't understand how to figure out what "c" is!!! Any help would be GREALY appreciated!

Thanks,
Katy
 
If I understand
Code: 
   -2 0 3 7 12 
FOD  2 3 4 5  (0-(-2)),(3-0),(7-3)
SOD   1 1 1   (3-2),(4-3),(5-4)

That gives .5n²+.5n-3 as the quadratic ax²+bx+c.

I can't help with what you quote the teacher saying. If you look at how the diferences are generated maybe you can change it?
Q<sub>n</sub> = Q<sub>n-1</sub> + FOD<sub>n-1</sub>
FOD<sub>n-1</sub> = FOD<sub>n-2</sub> + SOD<sub>n-2</sub>
is what I would say. I don't get the c

You can do Qsub-1 by typing Q<sub>1</sub>
 
Thanks for replying...I got the explicit formula question okay, the .5n²+.5n-3, I just dont know how to do the recursive version...
 
Isn't n the term number though? Sorry I'm still kind of confused :?

So then in this problem it would be

Q<sub>1</sub> = -2
Q<sub>n</sub> = Q<sub>n-1</sub> + what? the n changes, right? so how can you write a formula for it?

Thanks so much for helping me
 
I have no problem with having the term number as part of a recursive formula. You accepted it in the explicit formula. Why wouldn't it be acceptable recursively? (Rhetorical question. I don't really want to know :evil:)
---------------
Gene
 
Oh...good point...hmmm...I guess I don't see what distinguishes the recursive formula of one quadratic sequence from that of another then...it has to be unique to the sequence, right? like the explicit one is?
 
If I give you
1,4,9,16 the recursion would be
Q<sub>n</sub> = Q<sub>n-1</sub> + 2n-1
Different, no?
-----------------
Gene
 
Ohhhhhh!

And that looks like the weird form my teacher talked about! Cool! Thanks!
 
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