a 1=2

a2=2？ -2+ 1=3

a3=3？ -2*3+ 1=4

a4=4？ -3*4+ 1=5

....

Guess an=n+ 1

By mathematical induction, it holds when n = k.

So a(k+ 1)=(k+ 1)? -k (k+1)+1= (k+1) (k+1-k)+1= k+2.

Therefore, for any n, an=n+ 1 holds.