The question is...

1st term: -1

2nd term: 5

3rd term: 13

4th term: 23

5th term: 25

6th term: 35

7th term: 49

so what could nth term be?(Crying)

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- February 23rd 2008, 05:53 PMclarebear14Help me find the formula please!
The question is...

1st term: -1

2nd term: 5

3rd term: 13

4th term: 23

5th term: 25

6th term: 35

7th term: 49

so what could nth term be?(Crying) - February 23rd 2008, 06:26 PMTheEmptySet
- February 23rd 2008, 06:29 PMJaneBennet
Clearly the

*n*th term is

- February 23rd 2008, 06:31 PMxifentoozlerix
lol. lagrange ftw!

edit: btw, the fourth term's denominator should be -36 not -9.

- February 24th 2008, 01:40 AMCaptainBlack
Anything that you want.

Miss Bennet has put an interpolating polynomial through your seven points,

she could have in fact added an eighth point with value, say 7176, and put

a polynomial throught these eight points.

She could also have added:

where is any function on to her polynomial and it would still interpolate

your data exactly.

Without some background information constraining solutions, such puzzles have no unique solution.

RonL - February 24th 2008, 02:25 AMangel.white
- March 13th 2008, 11:34 PMJaneBennet
Just to clarify, the formula I provided above is on the assumption that the terms of your sequence satisfy a polynomial equation of degree at most 6.

In general, if the first*k*terms of a sequence are given, and it is assumed that the terms of the sequence satisfy a polynomial equation of degree at most , then the*n*th term of the sequence is

Alternatively, you could also let and solve for the coefficients by substituting the first given values – but this is going to take a hell of a much longer time. (Tongueout) - March 14th 2008, 08:31 AMCaptainBlack
This is the Lagrange interpolating polynomial. There is also a method due to Newton that uses the difference table to construct the interpolating polynomial. See here

RonL