37 Fit the cubic: Un = (2n3 - 9n2 + 16n + 6)/3 for n = 1, 2, 3, ...
There are many possible answers. One possibility is Un = (2n3 - 3n2 + n + 24)/6
25* * * * *24Using t(n) = (2n3 - 9n2 + 25n - 6)/6 for n = 1, 2, 3, ...Take your pick. I have given the justification for my answer.
11
There are infinitely many possible rules: there is one or more polynomials of every degree≥ 3 and then there are other possible functional relationships.There is only one polynomial of degree 3 and that isUn= (2n3- 15n2+ 19n + 12)/3 where n = 1, 2, 3, ...
The simplest polynomial, of an infinite number of possible solutions, is Un = (-2n3 + 12n2 - 7n + 6)/3
-31. The rule is t(n) = -2n3 + 12n2 -19n + 14 where n = 1, 2, 3, ...
5(25m3 + 2n3)
There are infinitely many possible answers. The simplest cubic polynomial is Un = (2n3 - 11n2 + 27n - 14)/2 for n = 1, 2, 3, 4.
2n2y2(2n3)(3y3)
2n3
The common name for a fatty acid with a c18 2n3 structure is alpha-linolenic acid. It is an essential omega-3 fatty acid that is important for proper brain function and reducing inflammation in the body.
37 Fit the cubic: Un = (2n3 - 9n2 + 16n + 6)/3 for n = 1, 2, 3, ...
There are many possible answers. One possibility is Un = (2n3 - 3n2 + n + 24)/6
Given any number at all, it is easy to find a polynomial of degree four that will fit the above numbers and the additional one as the first five of the sequence. A polynomial of degree 3 for the above number is Un = (2n3 - 11n2 + 23n - 12)/3 for n = 1, 2, ... and accordingly, the next number is 31.
(n2 + 2n - 1) (n2 + 2n - 1) = n4 + 2n3 - n2 + 2n3 + 4n2 - 2n - n2 - 2n + 1 = n4 + 4n3 + 2n2 - 4n + 1 try with n = 5: (5 squared + 10 - 1) squared = 34 squared = 1156 with formula (5^4) + (4 *(5^3)) + (2 * (5^2)) - (4 * 5) + 1 = 625 + 500 + 50 - 20 + 1 = 1156
25* * * * *24Using t(n) = (2n3 - 9n2 + 25n - 6)/6 for n = 1, 2, 3, ...Take your pick. I have given the justification for my answer.