-66 The sequence can be generated by the following quartic: t(n) = (-3n4 + 42n3 - 177n2 - 358n + 2808)/8 for n = 1, 2, 3, ...
The differences are not the same so the sequence is not arithmetic. The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence. The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.
It is possible to find a quartic equation (power 4) so that any fifth number is the next in the sequence. The cubic that fits these is Un = (n3 + 17n + 30)/6 for n = 1, 2, 3, ... and therefore, the next term is 40.
He is known for quartic equations.
No.
It depends on (a) the first five numbers of what and(b) what sort of sequence.ANY 5 numbers can be put into a quartic sequence. So the answer is: every time.
A quartic is an algebraic equation or function of the fourth degree.
-66 The sequence can be generated by the following quartic: t(n) = (-3n4 + 42n3 - 177n2 - 358n + 2808)/8 for n = 1, 2, 3, ...
The differences are not the same so the sequence is not arithmetic. The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence. The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.
A quartic.
It is possible to find a quartic equation (power 4) so that any fifth number is the next in the sequence. The cubic that fits these is Un = (n3 + 17n + 30)/6 for n = 1, 2, 3, ... and therefore, the next term is 40.
A quartic equation can be factored by grouping or using a substitution method. You can also use the rational root theorem to find potential rational roots and factorize the quartic equation accordingly. Alternatively, you can use numerical methods or technology to approximate the roots.
Luca Pacioli (1445-1515) discussed quartic equations, but did not have a general solution. Lodovico Ferrari (1522-1565) devised a solution.
Leonarda Burke has written: 'On a case of the triangles in-and-circumscribed to a rational quartic curve with a line of symmetry' -- subject(s): Quartic Curves, Triangle
He is known for quartic equations.
No.
Helen Grace Telling has written: 'The rational quartic curve in space of three and four dimensions' -- subject(s): Hyperspace, Quartic Curves