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There are infinitely many polynomials of order 5 that will give these as the first five numbers and any one of these could be "the" rule. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
One such is: U(n) = (5*n^5 - 15*n^4 + 85*n^3 - 201*n^2 + 250*n - 80)/8
another is U(n) = (4*n^5 - 80*n^4 + 340*n^3 - 900*n^2 + 1006*n - 330)/30
The simplest, based on a polynomial of order 1 is U(n) = 5 - 3n
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The given sequence appears to be increasing by 10 each time. To find the nth term, we can use the formula for arithmetic sequences: nth term = first term + (n-1) * common difference. In this case, the first term is 4 and the common difference is 10. Therefore, the nth term for this sequence would be 4 + (n-1) * 10, which simplifies to 10n - 6.
