A(n+ 1)-An=2(n+ 1)

That is, An-A(n- 1)=2n.

A(n- 1)-A(n-2)= 2(n- 1)

............

A3-A2=2*3

A2-A 1=2*2

Add up the above categories:

An-A 1=2*(2+3+...+n)= 2 *(2+n)*(n- 1)/2 =(n+2)(n- 1)

Therefore, An=A 1+(n+2)(n- 1).

Is there A 1= in the title?