An arithmetic progression has first term \(\log _ { 2 } 27\) and common difference \(\log _ { 2 } x\).
Show that the fourth term can be written as \(\log _ { 2 } \left( 27 x ^ { 3 } \right)\).
Given that the fourth term is 6, find the exact value of \(x\).
A geometric progression has first term \(\log _ { 2 } 27\) and common ratio \(\log _ { 2 } y\).
Find the set of values of \(y\) for which the geometric progression has a sum to infinity.
Find the exact value of \(y\) for which the sum to infinity of the geometric progression is 3 .
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