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Q: What is the nth term for the sequence 22 13 4 -5 -14?

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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.

They are: nth term = 6n-4 and the 14th term is 80

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. :)

Clearly here the nth term isn't n25.

The nth term is: 3n+2 and so the next number will be 20

The nth term in this sequence is 4n - 2.

14+9n

If the nth term is n*7 then the first 5 terms are 7, 14, 21, 28, 35.

The nth term of this sequence is 3n + 4

It is: nth term = -4n+14

t(n) = (-5n4 + 62n3 - 247n2 + 334n - 36)/6

t(n) = 10 - 6n where n = 1, 2, 3, ...

5, 8, 11, 14 and 17.

It is: nth term = 6n-4

t(n) = 6 + 8n

The nth term is 2 + 3n.

First look for the difference between the terms, for example the sequence: 5, 8, 11, 14... has a difference of 3. This means the sequence follows the 3 times table - i.e. 3n Now since we need the first term to be 5 we add 2 to our rule to make it work. So the nth term of this sequence is 3n + 2.

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

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

The differences are 3, 5, 7, 9,11, ... and the first term is -1; the nth term is: n² - 2

42

The nth term is 3n+2 and so the next number will be 17

25

It is: 9n+5 and so the next term is 50

The simplest polynomial, of an infinite number of possible solutions, is Un = (-2n3 + 12n2 - 7n + 6)/3