Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the nth is the given number. There are also non-polynomial solutions.
The simplest polynomial of smaller order is:
Un = (n2 + n + 4)/2 for n = 1, 2, 3, ...
The nth term is 18 -3n and so the next term will be 3
t(n) = 5n - 3
3n
12 - 5(n-1)
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
The nth term is 5n-3 and so the next term will be 22
5n - 3
tn=5n-3
The nth term is 18 -3n and so the next term will be 3
t(n) = 5n - 3
The nth term in the arithmetic progression 10, 17, 25, 31, 38... will be equal to 7n + 3.
3n
12 - 5(n-1)
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
7n - 4
If 3 is the first term, then the nth term is [ 3 x 2(n-1) ] .
The nth term is 4n - 3