Thread: Recursive formula

I have been working on this problem for about 5 days now and I still can't figure out the answer. One of my friends at school even asked someone from his work who is an electrical engineer that minored in math and he couldn't get it. the given series is 2,1,1,(15/7),390...

that is two, one, one, fifteen halfs, three hundred ninty...

if anyone can figure out the pattern and/or the formula for this series I would greatly appreciate it. I know that it is a sud n+1= ( )a sub n
but out side of that I have no idea what the solution could be. Any help on this would be greatly appreciated, again. Thanks.

Is there enough information??

fifteen halves or fifteen sevenths?

There is no unique way of solving these problems biohazard unless you give us more information. For example you can interpolate a polynomial p(n) such that a_n+1 = p(n) a_n etc. etc. etc.

Originally Posted by river_rat

There is no unique way of solving these problems biohazard unless you give us more information. For example you can interpolate a polynomial p(n) such that a_n+1 = p(n) a_n etc. etc. etc.

I think that is the way that it is supposed to bve done. But any solution to this problom would be helpful. In any form.

Originally Posted by Harold14370

fifteen halves or fifteen sevenths?

15/2 sorry. that is fifteen halfs. 7.5 is what I was thinking when I put that is. Sorry.

Please. Anything, even just a hint as to a pattern that I could do. something like an+1 = an*x^n or something. I still cant get it, and neither can anyone in my class but the teacher wont tell us until someone can bring in an answer for somewhere.

have you looked up interpolating polynomials?

Originally Posted by biohazard87

Please. Anything, even just a hint as to a pattern that I could do. something like an+1 = an*x^n or something. I still cant get it, and neither can anyone in my class but the teacher wont tell us until someone can bring in an answer for somewhere.

Honestly you could try to think of a bunch of things. As River suggested, just make a polynomial that passes through all the points to guess what the next point is. However there is no guarantee that will even be close to the answer you teacher is thinking.

I can almost assure you it won't be the formula your teacher has, but you have not been given the entire sequence anyway so what would the "correct" formula be?

Originally Posted by river_rat

have you looked up interpolating polynomials?

I am sorry, what is that and where would I look it up?