What is the nth term of the sequence -42 -36 -30 -24?

Answer 1

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)

Answer 2

To find the nth term of a sequence, we first need to identify the pattern or rule by which the sequence is increasing or decreasing. In this case, the sequence is decreasing by 6 each time. So, the common difference between each term is -6. To find the nth term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference. Plugging in the values, we get a_n = -42 + (n-1)(-6) = -42 - 6n + 6 = -6n - 36. Therefore, the nth term of the sequence is -6n - 36.

Answer 3

The nth term of the sequence -42 -36 -30 -24 is -6(n-1) - 42