1, the arrangement from left to right is positive, negative, positive, negative, positive and negative. . Therefore, the positive or negative judgment of the nth number is (-1) (n- 1) or it can be written as (-1) (n+ 1).

2. Molecular law: 2, 4, 8, 16, ... It can be seen that it is 2 1, 2 2, 2 3, ... So the nth number of molecules is 2 n.

3. Denominator Law: 25 10 17 ... It can be seen that it is 1 2+ 1, 2 2+ 1, 3 2+ 1 ... So the denominator of the nth number is n.

So the nth number is:

(- 1)^(n- 1)* 2^n/( n^2+ 1)

It can also be written as (-1) (n+1) * 2n/(n 2+1).