8. (i) An arithmetic series has first term \(a\) and common difference \(d\).
Prove that the sum to \(n\) terms of this series is
$$\frac { n } { 2 } \{ 2 a + ( n - 1 ) d \}$$
(ii) A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is given by
$$u _ { n } = 5 n + 3 ( - 1 ) ^ { n }$$
Find the value of
- \(u _ { 5 }\)
- \(\sum _ { n = 1 } ^ { 59 } u _ { n }\)