There are infinitely many polynomials of order 5 that will give these as the first five numbers and any one of these could be "the" rule. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
One such is: U(n) = (5*n^5 - 15*n^4 + 85*n^3 - 201*n^2 + 250*n - 80)/8
another is U(n) = (4*n^5 - 80*n^4 + 340*n^3 - 900*n^2 + 1006*n - 330)/30
The simplest, based on a polynomial of order 1 is U(n) = 5 - 3n
The nth term in this arithmetic sequence is an=26+(n-1)(-8).
It is: nth term = -4n+14
3n-2
The nth term is (2n - 12).
You can see that you add 10 to the previous term to get the next term. Term number 1 2 3 4 Term 4 14 24 34 You can also say: Term number 1 2 3 4 Term 0*10+4 1*10+4 2*10+4 3*10+4 So the nth term would be 10(n-1)+4 Or if you expand it, it's 10n-6
The nth term in this arithmetic sequence is an=26+(n-1)(-8).
It is: nth term = -4n+14
3n-2
The nth term is (2n - 12).
You can see that you add 10 to the previous term to get the next term. Term number 1 2 3 4 Term 4 14 24 34 You can also say: Term number 1 2 3 4 Term 0*10+4 1*10+4 2*10+4 3*10+4 So the nth term would be 10(n-1)+4 Or if you expand it, it's 10n-6
f = 10n + (n - 1)^2 For n=10 f = 10(10) + (10 - 1)^2 f = 181
1, 3, 6, 10, ... The nth term is n*(n+1)/2
The sequence has a difference of 10, so the nth term starts with 10n. Then to get to -8 from 10 you need to subtract 18. So the nth term is 10n - 18.
2n^2-1
The nth term of the sequence is (n + 1)2 + 2.
1st term= 3 2nd term = 5 Nth term = 2n+1 10th term= 21 = 2(10)+1
The nth term would be -2n+14 nth terms: 1 2 3 4 Sequence:12 10 8 6 This sequence has a difference of -2 Therefore it would become -2n. Replace n with 1 and you would get -2. To get to the first term you have to add 14. Therefore the sequence becomes -2n+14. To check your answer replace n with 2, 3 or 4. You will still obtain the number in the sequence that corresponds to the nth term. :)