What is the nth term for 22 19 16 13 19?

Answer 1

To find the nth term in a sequence, we first need to identify the pattern. In this sequence, it appears to be alternating between subtracting 3 and adding 6. Therefore, the nth term can be calculated using the formula: nth term = 22 + (n-1)(-3)^n-1 for odd values of n, and nth term = 19 + (n-2)(6)^n-2 for even values of n.

Answer 2

One such formula is:

t(n) = (3n^4 - 30n³ + 105n² -174n + 272)/8

which is only valid for n = 1, 2, 3, 4, 5.

If you give another term for n=6, there is no guarantee that this formula will work.

Answer 3

There are infinitely many polynomials of order 5 that will give these as the first five numbers and any one of these could be "the" rule for the nth term. 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. And that assumes that the solution is a polynomial, not some other function of n.
The simplest solution for the nth term, based on a polynomial of degree 4, is
U(n) = (3*n^4 - 30*n^3 + 105*n^2 - 174*n + 272)/8

Answer 4

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