- In this question you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
A geometric series has common ratio \(r\) and first term \(a\).
Given \(r \neq 1\) and \(a \neq 0\)
- prove that
$$S _ { n } = \frac { a \left( 1 - r ^ { n } \right) } { 1 - r }$$
Given also that \(S _ { 10 }\) is four times \(S _ { 5 }\)
- find the exact value of \(r\).