Question 1173421
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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.<br>
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.<br>
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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<br>
<h2><b><i>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,</h2></b></i> then the problem can be solved.<br>
If you use a matrix to solve the polynomial equation<br>
{{{p(x) = ax^4+bx^3+cx^2+dx+e}}}<br>
using
p(1)=73
p(2)=74
p(3)=88
p(4)=99
p(5)=108<br>
and use the resulting polynomial to find the next term, you will find that<br>
p(6) = 133<br>
as you know it is supposed to be.<br>