How do we know this? For the recursive definition, we need to specify \(a_0\text{.}\) Then we need to express \(a_n\) in terms of \(a_{n-1}\text{.}\) If we call the first term \(a\text{,}\) then \(a_0 = a\text{.}\) For the recurrence relation, by the definition of an arithmetic sequence, the difference between successive terms is some constant, say \(d\text{.}\) So \(a_n - a_{n-1} = d\text{,}\) or in other words,