There are infinitely many polynomials of order 4 (or higher) that will give these as the first four 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.
The simplest rule is a linear polynomial U(n) = 6*(2 - n) for n = 1 , 2, 3, ...
10-2x for x = 0, 1, 2, 3, ... Since the domain of an arithmetic sequence is the set of natural numbers, then the formula for the nth term of the given sequence with the first term 10 and the common difference -2 is an = a1 + (n -1)(-2) = 10 - 2n + 2 = 12 - 2n.
The nth term is 2n2. (One way to find that is to notice at all the numbers are even, then divide them by 2. The sequence becomes 1, 4, 9, 16, 25, which are the square numbers in order.)
According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.The simplest rule is un = 18 - 3n
There can be no answer because a number sequence, in itself, is not a question.
Sn = -8n + 2S0 = -8(0) + 2 = 2S1 = -8(1) + 2 = -6S2 = -8(2) + 2 = -14S3 = -8(3) + 2 = -22S4 = -8(4) + 2 = -30S5 = -8(5) + 2 = -38
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.