11.
A geometric sequence, \(S _ { 1 }\), has first term \(a\) and common ratio \(r\) where \(a \neq 0\) and \(r \in ( - 1,1 )\)
A new sequence, \(S _ { 2 }\), is formed by squaring each term of \(S _ { 1 }\)
- Given that the sum to infinity of \(S _ { 2 }\) is twice the sum to infinity of \(S _ { 1 }\), show that \(a = 2 ( 1 + r )\)
Fully justify your answer.
- Determine the set of possible values for \(a\).
\section*{Additional Answer Space }
\section*{Additional Answer Space }