10. A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = 4
u _ { n + 1 } & = \frac { 2 u _ { n } } { 3 } , \quad n \geqslant 1
\end{aligned}$$
- Find the exact values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\)
- Find the value of \(u _ { 20 }\), giving your answer to 3 significant figures.
- Evaluate
$$12 - \sum _ { i = 1 } ^ { 16 } u _ { i }$$
giving your answer to 3 significant figures.
- Explain why \(\sum _ { i = 1 } ^ { N } u _ { i } < 12\) for all positive integer values of \(N\).