That is to say, A (S+ 1)-A (S) = 2+S, and s is counted from 1.

You can see it by listing more items:

A noun

-A(N- 1)=N+ 1

A(N- 1)-A(N-2)=N

...

Answer (2)

-A( 1)

=3

Add them all up to get a (n)-a (1) = 3+4+...+(n+1).

So A(N)=3+(N+4)(N- 1)/2.

Check the case where n is smaller again and find that there is no problem, so the answer is this.