- A geometric sequence has first term \(a\) and common ratio \(r\)
Given that \(S _ { \infty } = 3 a\)
- show that \(r = \frac { 2 } { 3 }\)
Given also that
$$u _ { 2 } - u _ { 4 } = 16$$
where \(u _ { k }\) is the \(k ^ { \text {th } }\) term of this sequence,
- find the value of \(S _ { 10 }\) giving your answer to one decimal place.