recursive definition for arithmetic sequence
An arithmetic sequence is a linear function. Instead of y=mx+b, we write a n =dn+c where d is the common difference and c is a constant (not the first term of the sequence, however). A recursive definition, since each term is found by adding the common difference to the previous term is a k+1 =a k +d. For any term in the sequence, we've added the difference one less time than the number of the term. For example, for the first term, we haven't added the difference at all (0 times).