Item 1.

\(5-2 = 3\text{,}\) \(8-5 = 3\text{,}\) etc. To get from each term to the next, we add three, so \(d = 3\text{.}\) The recursive definition is therefore \(a_n = a_{n-1} + 3\) with \(a_0 = 2\text{.}\) The closed formula is \(a_n = 2 + 3n\text{.}\)