Looking for patterns?

The second question is relatively simple. Write the results directly. a(n)=n？ .

Let's talk about the first question.

a(3)= 3×a(2)-a( 1)= 13；

a(4)= 3×a(3)-a(2)= 34；

a(5)=3×a(4)-a(3)=89 .

To sum up, the law is like this

a( 1)= 2； a(2)= 5；

a(n+2)=3×a(n+ 1)-a(n).

Irrational numbers will appear in the general formula, so they are not deduced.