8 An arithmetic series has first term \(a\) and common difference \(d\). The sum of the first 5 terms of the series is 575 .
- Show that \(a + 2 d = 115\).
- Given also that the 10th term of the series is 87, find the value of \(d\).
- The \(n\)th term of the series is \(u _ { n }\). Given that \(u _ { k } > 0\) and \(u _ { k + 1 } < 0\), find the value of \(\sum _ { n = 1 } ^ { k } u _ { n }\).
[0pt]
[5 marks]