- A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } \ldots\) is defined by
$$\begin{aligned}
u _ { 1 } & = 35
u _ { n + 1 } & = u _ { n } + 7 \cos \left( \frac { n \pi } { 2 } \right) - 5 ( - 1 ) ^ { n }
\end{aligned}$$
- Show that \(u _ { 2 } = 40\)
- Find the value of \(u _ { 3 }\) and the value of \(u _ { 4 }\)
Given that the sequence is periodic with order 4
- write down the value of \(u _ { 5 }\)
- find the value of \(\sum _ { r = 1 } ^ { 25 } u _ { r }\)