Write out the first 5 terms (starting with \(a_0\) ) of each of the sequences described below. Then give either a closed formula or a recursive definition for the sequence (whichever is NOT given in the problem).
\(a_n = \frac{1}{2}(n^2 + n)\text{.}\)
\(a_n = 2a_{n-1} - a_{n-2}\) with \(a_0 = 0\) and \(a_1 = 1\text{.}\)
\(a_n = na_{n-1}\) with \(a_0 = 1\text{.}\)