Any number that you choose can be the nth number. It is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question followed by the chosen number in the nth position. There are also non-polynomial solutions. 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.
For example, U(n) = (3*n^4 - 30*n^3 + 105*n^2 - 126*n - 120)/4 gives the next number as 0orU(n) = (19*n^4 - 190*n^3 + 665*n^2 - 806*n - 696)/24 gives the next number as 1and so on.
The simplest solution, though, based on a polynomial of order 3 is U(n) = 6*(x - 8)
The nth term of the sequence -42 -36 -30 -24 is -6(n-1) - 42
6n+10
When n=30, 3n-1 = 89 .
There are infinitely many possible answers. But the simplest is Un = 33 - 3n for n = 1, 2, 3, ...
t(n) = 6 + 8n
fsedaz sd
90
6n+10
There are not enough numbers to be certain. The rule for the nth term could be Subtract 6 from the previous term giving 30, 24, 18, etc or Multiply previous term by 0.8 giving 30, 24, 21.6, etc etc
Clearly here the nth term isn't n25.
When n=30, 3n-1 = 89 .
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
There are infinitely many possible answers. But the simplest is Un = 33 - 3n for n = 1, 2, 3, ...
The nth term of the sequence is 3n-8 and so the 30th term is 3*30 -8 = 82
32, 60, 88, 116, 144
t(n) = 6 + 8n
fsedaz sd
This is an arithmetic progression. In general, If an A.P. has a first term 'a', and a common difference 'd' then the nth term is a + (n - 1)d. In the sequence shown in the question, the first term is 0 and the common difference is 5, therefore the nth term is, 0 + (n - 1)5. This can be rearranged to read : 5(n - 1) For example : the 7th term is 30 : 5(7 - 1) = 5 x 6 = 30.