Item 2.

The sequence of first differences is \(7, 43, 133, 301, 571,\ldots\text{.}\) The second differences are: \(36, 90, 168, 270,\ldots\text{.}\) Third difference: \(54, 78, 102,\ldots\text{.}\) Fourth differences: \(24, 24, \ldots\text{.}\) As far as we can tell, this sequence of differences is constant so the sequence is \(\Delta^4\)-constant and as such the closed formula is a degree 4 polynomial.