14.
The sum to infinity of a geometric series is 96
The first term of the series is less than 30
The second term of the series is 18
- Find the first term and common ratio of the series.
[0pt]
[4 marks] - Show that the \(n\)th term of the series, \(u _ { n }\), can be written as
$$u _ { n } = \frac { 3 ^ { n } } { 2 ^ { 2 n - 5 } }$$
[3 marks]
- (ii) Hence show that
$$\log _ { 3 } u _ { n } = n \left( 1 - 2 \log _ { 3 } 2 \right) + 5 \log _ { 3 } 2$$