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what is next number and find what formula used?

by meer
(india)











































1)3375/10 07/07/10 2, 5, 7, 29, 33, 54
2)3376/10 10/07/10 1, 6, 7, 14, 22, 32
3)3377/10 11/07/10 4, 16, 17, 21, 47, 50
4)3378/10 14/07/10 14, 18, 25, 43, 54, 55
5)3379/10 17/07/10 3, 7, 8, 18, 49, 52
6)3380/10 18/07/2010 2, 24, 25, 29, 38, 55
7)3381/10 21/07/2010 ??

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Aug 22, 2010
series & sequence formulas
by: Staff

THE NEXT NUMBER – series & sequence formulas

The question:

What is next number and find what formula used?

1) 3375/10……07/07/10……2, 5, 7, 29, 33, 54
2) 3376/10……10/07/10……1, 6, 7, 14, 22, 32
3) 3377/10……11/07/10……4, 16, 17, 21, 47, 50
4) 3378/10……14/07/10……14, 18, 25, 43, 54, 55
5) 3379/10……17/07/10……3, 7, 8, 18, 49, 52
6) 3380/10……18/07/2010…2, 24, 25, 29, 38, 55
7) 3381/10……21/07/2010…??

The answer:

Since these data sets are not known sequences (such as standard arithmetic or geometric sequences, harmonic series, alternating series, Fibonacci Sequence, etc.), a more general approach to evaluating the function involved is probably easiest.

Other than trial and error, the most general approach I know of involves differentiating the curve (finding the slope of the curve) formed by the data set over and over until you reach a constant value. At that point you can write an equation for the data points.

One of the places this approach is fully explained is on the following website:

http://www.johansens.us/sane/technotes/formula.htm

Not only is this process explained on the website, but a handy calculator is also provided here:

http://www.electrictactics.com/poly/polyin.html


In general, you should have more than 6 data points to use the on-line calculator. However I have used this calculator develop a function to predict the beginning value of #7 by inputting the beginning values of #1 through #6:

y = +3/4 x5 -301/24 x4 +463/6 x3 -5159/24 x2 +3223/12 x -117





Thanks for writing.


Staff
www.solving-math-problems.com


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