t(n) = (-5n4 + 62n3 - 247n2 + 334n - 36)/6
They are: nth term = 6n-4 and the 14th term is 80
5, 8, 11, 14 and 17.
By varying the parameters of a quartic polynomial, the nth term can be made whatever you like. But, taking the simplest solution, Un = 2 - 4n for
The simplest rule is Un = 26 - 8n for n = 1, 2, 3, ... but it is always possible to fit a polynomial of degree 5 to the given sequence of numbers along with any sixth number.
Given ANY number at all, it is possible to find a cubic polynomial such that that particular number is the nth number in a sequence starting with the above three. The simplest rule, however, is Un = 5n + 9
It is: 26-8n
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. :)
The given sequence (7, 14, 21, 28, 35,....) is an arithmetic sequence where each term increases by 7. The nth term of the given sequence is 7n
They are: nth term = 6n-4 and the 14th term is 80
The nth term of this sequence is 3n + 4
It is: nth term = -4n+14
This is an arithmetic sequence which starts at 14, a = 14, and with a common difference of -1, d = -1. We can use the nth term formula an = a + (n - 1)d to get an = 14 + (n - 1)(-1) = 14 - n + 1 = 15 - n.
Clearly here the nth term isn't n25.
t(n) = 10 - 6n where n = 1, 2, 3, ...
The nth term is: 3n+2 and so the next number will be 20
You can see that all the numbers go up by 7. This means that the first part of the nth term rule for this sequence is 7n. Now, you have to find out how to get from 7 to 3, 14 to 10, 21 to 17 ... this is because we are going up in the 7 times table. To get from the seventh times table to the sequence, you take away four. So the answer is : 7n-4
25