9 The first term of a geometric series is 12 and the common ratio of the series is \(\frac { 3 } { 8 }\).
- Find the sum to infinity of the series.
- Show that the sixth term of the series can be written in the form \(\frac { 3 ^ { 6 } } { 2 ^ { 13 } }\).
- The \(n\)th term of the series is \(u _ { n }\).
- Write down an expression for \(u _ { n }\) in terms of \(n\).
- Hence show that
$$\log _ { a } u _ { n } = n \log _ { a } 3 - ( 3 n - 5 ) \log _ { a } 2$$
(4 marks)