SOLUTION: Hi Tutors, I need help with solving a sequence below. 73,74,88,99,108 note that I am aware that the next term is 133 and that is the number I am looking for, however, these n

Question 1173421: Hi Tutors, I need help with solving a sequence below.
73,74,88,99,108
note that I am aware that the next term is 133 and that is the number I am looking for, however, these numbers are actually decimals and the program I used to solve them doesn't allow decimals. Actual sequence is (73.1771,73.9964,87.9820,99.0045,108.9807) and the actual term I am looking for is 133.2632 which is what I am looking for but I cannot figure out how I got 133.2632.
So I need help with solving the decimal sequence to give me 133.2632 and also the next term after that which is 209 when using the first sequence with no decimal points.
Also to note, I rounded up 2nd and 3rd numbers from 73.9964 to 74 and 87.9820 to 88 respectively and I did get 133 but I did not round off 108.
Thank you
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

To begin with, if the original problem simply says to find the next term in the sequence, then the problem is invalid, because any next number would form a valid sequence.

You don't say anything about how you did your calculations, other than to say that you used a program. So we can't help you with figuring out what to do with the numbers you came up with.

-------------------------------------------------------------

The given sequence is a sequence of five numbers. Any sequence of five numbers can be produced by a unique polynomial of degree 4; it can also be produced by an infinite number of polynomials of degrees higher than 4. So

if the original problem was to find the next number in the sequence, given that the given five numbers were produced by a polynomial of degree 4,

then the problem can be solved.

If you use a matrix to solve the polynomial equation

using
p(1)=73
p(2)=74
p(3)=88
p(4)=99
p(5)=108

and use the resulting polynomial to find the next term, you will find that

p(6) = 133

as you know it is supposed to be.

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