There are infinitely many sequence that will fit the above four numbers so there are infinitely many possible answers.
For example, the sequence could be based on the rule
Un = (-7n4 + 70n3 -233n2 + 338n - 168)/12 for n = 1, 2, 3, ...
It is probably based on
Un = n*(n+1) for n = 1, 2, 3, ...
The nth term of that series is (24 - 6n).
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
7 - 4n where n denotes the nth term and n starting with 0
This is the Fibonacci sequence, where the number is the sum of the two preceding numbers. The nth term is the (n-1)th term added to (n-2)th term
The pattern for the sequence 0 0 1 3 6 is that each term is obtained by adding the previous term multiplied by its position in the sequence (starting from 1). In other words, the nth term is given by n*(n-1)/2.
24 - 6n
18 - 6n
The nth term of that series is (24 - 6n).
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
7 - 4n where n denotes the nth term and n starting with 0
If the nth term is 8 -2n then the 1st four terms are 6, 4, 2, 0 and -32 is the 20th term number
An = 2(n - 1)2 + 2(n - 1) = 2n(n - 1)
-4, -3, 0, 5, 12, 21, 32
This is the Fibonacci sequence, where the number is the sum of the two preceding numbers. The nth term is the (n-1)th term added to (n-2)th term
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.
16 - 4nor4 (4 - n)
The pattern for the sequence 0 0 1 3 6 is that each term is obtained by adding the previous term multiplied by its position in the sequence (starting from 1). In other words, the nth term is given by n*(n-1)/2.