7. A geometric series has first term 1200. Its sum to infinity is 960 .
- Show that the common ratio of the series is \(- \frac { 1 } { 4 }\).
- Find, to 3 decimal places, the difference between the ninth and tenth terms of the series.
- Write down an expression for the sum of the first \(n\) terms of the series.
Given that \(n\) is odd,
- prove that the sum of the first \(n\) terms of the series is
$$960 \left( 1 + 0.25 ^ { n } \right)$$