Q: What is the first 5 numbers to this sequence equals 5n-4?

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t(n) = (5n4 - 10n3 + 55n2 - 50n + 24)/24 where n = 1, 2, 3, ...

It depends on what number you would like. Given any real number, it is possible to find a real polynomial of degree 5 that will go through these 5 and the nominated 6th number. Fitting a polynomial of degree 4 to these numbers, the fitted next number is 44. Un = (-5n4 + 58n3 - 232n2 + 371n - 186)/6 for n = 1, 2, 3, ... ------------------------ All the above is true but just in case the simple answer is the real answer, I'd bet on 4 (then -2, 5,-3)

It could be Un = (-3n4 + 30n3 - 105n2 + 168n - 80)/2 or Un = (-5n4 + 50n3 - 175n2 + 286n - 136)/4 or any one of infinitely more polynomials of order >1, or other types of functions. The simplest polynomial solution is Un = 9n - 4 or any

Related questions

t(n) = (-5n4 + 62n3 - 247n2 + 334n - 36)/6

Next is 18. The polynomial rule is Un = (-5n4 + 74n3 - 301n2 + 478n - 24)/24 for n = 1, 2, 3, ...

There are many possible answers. If the sequence is generated by the quartic polynomial: t(n) = (5n4 - 38n3 + 127n2 - 166n + 96)/24 for n = 1, 2, 3, ... the next number will be 81

The next number in the sequence can be determined in infinitely many ways. One possible answer is the quartic polynomial, Un = (5n4 - 60n3 + 246n2 - 403n + 248)/2 for n = 1 , 2, 3, ... U6, the next term is 103.

t(n) = (5n4 - 10n3 + 55n2 - 50n + 24)/24 where n = 1, 2, 3, ...

Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the sixth is the given number. That is, it is easy to find a rule so that any number can be the "next" in the sequence.However, the simplest polynomial of order 4 is:Un = (5n4 - 54n3 + 217n2 - 312n + 240)/12 for n = 1, 2, 3, ...and, accordingly, U6 = 83.

Given any number it is possible to find a polynomial of order 5 that will generate the above five numbers and the additional one. The simplest polynomial of order 4 is U4 = (-5n4 + 58n3 - 232n2 + 371n - 186)/6 for n = 1, 2, 3, ... Accordingly, the next number is -44.

21 t(n) = (-5n4 + 66n3 - 271n2 + 450n - 216)/24, where n = 1, 2, 3, ...

50. The position to value rule used is Un = (3n5 - 5n4 - 285n3 + 1745n2 - 3138n + 1800)/120 for n = 1, 2, 3, ...

It could be any number you like since it is always possible to find a polynomial of order 5 that will fit the given 5 numbers and any sixth number. Fitting the following polynomial, of order 4, shows that the next term should be 110. Un = (5n4 - 50n3 + 195n2 - 358 + 328)/8 for n = 1, 2, 3, ...

Unfortunately, the browser used by Answers.com for posting questions is incapable of accepting mathematical symbols. This means that we cannot see the mathematically critical parts of the question. We are, therefore unable to determine what exactly the question is about and so cannot give a proper answer to your question.

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