2 A sequence is defined by the recurrence relation \(t _ { n + 1 } = \frac { t _ { n } } { n + 3 }\) for \(n \geqslant 1\), with \(t _ { 1 } = 8\).
Verify that the particular solution to the recurrence relation is given by \(t _ { n } = \frac { a } { ( n + b ) ! }\) where \(a\) and \(b\) are constants whose values are to be determined.