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Can 3n to the second power over 12n to the third be simplified?
Yes. 3n2/12n3 = 1/4n
What is the nth term for 1 7 13 31 49?
There are infinitely many possible answers. the simplest polynomial is Un = -n4 + 12n3 - 47n2 + 78n - 41
What is the function rule if X is -3 2 4 4.5 and Y is 8 3 1 5?
The rule, using a polynomial function of the lowest order is Un = (12n3 - 36n2 - 145n + 413)/25
What is the next number in the series 3 6 9 15 21?
The next number is 18. This is obtained by fitting the quartic polynomial t(n) = (-n4 + 12n3 - 47n2 + 84n - 36)/4 for n = 1, 2, 3, etc.
What is the next number in the sequence 298 209 125 58 and -4?
The quartic: t(n) = -n4 + 12n3 - 44.5n2 - 24.5n + 356 fits the data for n = 1, 2, 3, ... Putting n = 6 gives t(6) = -97 NB: A more popular version of this question has 129 as the third number.
What number comes next in 1 3 6 8 11?
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 next is the given number. There are also non-polynomial solutions.The simplest polynomial rule isUn = (n4 - 12n3 + 50n2 - 69n + 36)/6 which gives the next number as 21
