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What is two-third of the cube of a number?
2/3n3
What is the next term in this sequence 7 12 30 70 141 252?
Given any number, it is always possible to find a polynomial of degree 6 that will fit the above numbers and the additional given number.The simplest position to value rule, in polynomial form, for the above sequence isUn = (3n3 - 5n2 + 4n - 12)/2 for n = 1, 2, 3, ...and accordingly, U7 = 412.
What is the pattern in one eighth two sevenths one half and four fifths?
One possible answer is: Un = (3n3 - 3n2 + 78n - 8)/560 for n = 1, 2, 3, 4.
What is the next number in this pattern 3 12 35 63?
Given ANY number, it is easy to find a polynomial of order 4 such that if you use it as a position to value rule you get the four given numbers and your chosen one as the fifth. As a result, any number can be the next in the sequence. The simplest polynomial of order 3 for the above four numbers is: Un = (-3n3 + 32n2 - 57n + 34)/2 for n = 1, 2, 3, ... Accordingly, the next number is 87.
The product of four consective integers is one less than a perfect square?
Suppose the smallest of the integers is n. Then the product of the four consecutive integers is n*(n+1)*(n+2)*(n+3) =(n2+3n)(n2+3n+2) = n4+6n3+11n2+6n So product +1 = n4+6n3+11n2+6n+1 which can be factorised as follows: n4+3n3+n2 +3n3+9n2+3n + n2+3n+1 =[n2+3n+1]2 Thus, one more that the product of four consecutive integers is a perfect square.
What number comes next in the sequence 32-55-165-1848?
6590. One possible sequence is 2472/3N3 - 14421/2N2 + 26165/6N - 1390
What is two-third of the cube of a number?
2/3n3
What is the GCF of 6n to the third power and 9n to the third power?
The GCF is 3n3
What is the next term in this sequence 7 12 30 70 141 252?
Given any number, it is always possible to find a polynomial of degree 6 that will fit the above numbers and the additional given number.The simplest position to value rule, in polynomial form, for the above sequence isUn = (3n3 - 5n2 + 4n - 12)/2 for n = 1, 2, 3, ...and accordingly, U7 = 412.
What is the pattern in one eighth two sevenths one half and four fifths?
One possible answer is: Un = (3n3 - 3n2 + 78n - 8)/560 for n = 1, 2, 3, 4.
What is the next number in this pattern 3 12 35 63?
Given ANY number, it is easy to find a polynomial of order 4 such that if you use it as a position to value rule you get the four given numbers and your chosen one as the fifth. As a result, any number can be the next in the sequence. The simplest polynomial of order 3 for the above four numbers is: Un = (-3n3 + 32n2 - 57n + 34)/2 for n = 1, 2, 3, ... Accordingly, the next number is 87.
The product of four consective integers is one less than a perfect square?
Suppose the smallest of the integers is n. Then the product of the four consecutive integers is n*(n+1)*(n+2)*(n+3) =(n2+3n)(n2+3n+2) = n4+6n3+11n2+6n So product +1 = n4+6n3+11n2+6n+1 which can be factorised as follows: n4+3n3+n2 +3n3+9n2+3n + n2+3n+1 =[n2+3n+1]2 Thus, one more that the product of four consecutive integers is a perfect square.
What is the missing number in this sequence 1 13 33 53?
The answer depends on which number is missing. Even if the location of the gap is know, there are infinitely many possible solutions. The solutions listed below are polynomials of the lowest degree. First: 5 using the rule Un = (-4n3 + 48n2 - 128n + 99)/3 Second: 0 using the rule Un = (-7n3 + 84n2 - 209n + 138)/6 Third: 21.666 (recurring) using the rule Un = (3n3 - 23n2 + 84n - 61)/3 Fourth: 50 using the rule Un = (-11n3 + 90n2 - 121n + 48)/6 Fifth: 65 using the rule Un = (-4n3 + 36n2 - 44n + 15)/3
What is the next number in the series 6 3 8 12?
Any number of your choice. It is possible to find a quartic (order 4) polynomial that will fit the given 4 points and any other. There is only one cubic that will do the trick: Un = (-3n3 + 26n2 - 63n + 52)/2 for n = 1, 2, 3, ... and according to it U5 = 6.
What is two-thirds the cube of a number?
Two-thirds the cube of a number can be calculated by first finding the cube of the number, then multiplying that result by two, and finally dividing the product by three. Mathematically, this can be represented as (2/3) * (x^3), where x is the number in question. This expression simplifies to (2x^3) / 3. This calculation results in a value that is two-thirds of the cube of the original number.
What is the fourth difference sequence formula?
A solution for 4th difference sequence is:Formula: Tn = an4+ bn3+ cn2 + dn + e1st term = a + b + c + d + e1st difference = 15a + 7b + 3c + d2nd difference = 50a + 12b + 2c3rd difference = 60a + 6b4th difference = 24aExample:Tn (term number) = 1 2 3 4 5 6 7Sequence = 1 41 209 643 1529 3101 56411st difference = 40 168 434 886 1572 25402nd difference = 128 266 452 686 9683rd difference = 138 186 234 2824th difference = 48 48 48Step 1: 4th difference = 24a:24a = 48a = 2Step 2: 3rd difference = 60a + 6b:60(2) + 6b = 138b = 3Step 3: 2nd difference = 50a + 12b + 2c:50(2) + 12(3) + 2c = 128c = -4Step 4: 1st difference = 15a + 7b + 3c + d:15(2) + 7(3) + 3(-4) + d = 40d = 1Step 5: 1st 1st term = a + b + c + d + e:2 + 3 - 4 + 1 + e = 1e = -1Answer:Tn = 2n4+ 3n3- 4n2 + n - 1
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