Precalculus (6th Edition) Blitzer

Arithmetic sequence and the common difference is $d=1$.
We are given that $a_n=n-3$ Here, we have the first four terms $a_1=-2, a_2=-1,a_3=0,a_4=1$ when $n=1,2,3,4$ Now, subtract each two consecutive terms as below: $a_2-a_1=-1+2=1; a_3-a_2=0+1=1; a_4-a_3=1-0=1$ We can see that this is an arithmetic sequence and the common difference is $d=1$.