The first one is arithmetic progression with a difference of 4, so f (n) = 5+4 (n-1) = 4n+1;

The second is arithmetic progression, with a difference of -5, so f (n) = 2-5 (n-1) = 7-5n;

A universal formula is impossible. The simplest method is to draw the corresponding points in the coordinate system, then look at the general distribution, then choose the corresponding function, and finally find the specific function according to the numerical value. For example, for these two problems, the distribution of points is basically a straight line, and the corresponding function is a linear function, that is, geometric series, which can be solved by y = ax+b.

The set n of natural numbers refers to a set that satisfies the following conditions:

① There is an element in n, which is recorded as 1.

② Every element in n can find an element in n as its successor.

③ 1 is the successor of 0.

④0 is not the successor of any element.

⑤ Different elements have different successors.

⑥ (inductive axiom) Any subset m of n, if 1∈M, and as long as X is in M, it can be deduced that the successor of X is also in M, then M = N. ..