6. A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = 36
u _ { n + 1 } & = \frac { 2 } { 3 } u _ { n } , \quad n \geqslant 1
\end{aligned}$$
- Find the exact simplified values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\)
- Write down the common ratio of the sequence.
- Find, giving your answer to 4 significant figures, the value of \(u _ { 11 }\)
- Find the exact value of \(\sum _ { i = 1 } ^ { 6 } u _ { i }\)
- Find the value of \(\sum _ { i = 1 } ^ { \infty } u _ { i }\)