9. The first term of an arithmetic series is \(a\) and the common difference is \(d\).
The 18th term of the series is 25 and the 21st term of the series is \(32 \frac { 1 } { 2 }\).
- Use this information to write down two equations for \(a\) and \(d\).
- Show that \(a = - 17.5\) and find the value of \(d\).
The sum of the first \(n\) terms of the series is 2750 .
- Show that \(n\) is given by
$$n ^ { 2 } - 15 n = 55 \times 40 .$$
- Hence find the value of \(n\).