6 In this question you must show detailed reasoning.
A sequence \(S\) has terms \(u _ { 1 } , u _ { 2 } , u _ { 3 } \ldots\) defined by \(u _ { 1 } = 500\) and \(u _ { n + 1 } = 0.8 u _ { n }\).
- State whether \(S\) is an arithmetic sequence or a geometric sequence, giving a reason for your answer.
- Find \(u _ { 20 }\).
- Find \(\sum _ { n = 1 } ^ { 20 } u _ { n }\).
- Given that \(\sum _ { n = k } ^ { \infty } u _ { n } = 1024\), find the value of \(k\).