Sequence and Series - Proving the progression

The first four terms of a sequence are \(18, 54, 162, 486\).

1. Use all four terms to show that this is a geometric sequence.[2]
2. 1. Find an expression for the \(n^{\mathrm{th}}\) term of this geometric sequence.
   2. If the \(n^{\mathrm{th}}\) term of the sequence is \(1 \ 062 \ 882\), find the value of \(n\).[4]