(a) A geometric progression has common ratio \(r\) and first term \(a\), where \(a \neq 0\). The 4th term is -8 times the 7th term. (i) Find the value of \(r\). (ii) The sum of the first 5 terms of this progression is \(\frac{99}{32}\). Find the value of \(a\). (b) The first three terms of a different geometric progression are \(\cos \theta \sin \theta, \cos \theta \sin ^{3} \theta\) and \(\cos \theta \sin ^{5} \theta\), for \(0<\theta<\frac{\pi}{2}\). Show that the sum to infinity of this progression is \(\tan \theta\).

2026 - M/J - 0606/11 | Q9

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(a) A geometric progression has common ratio \(r\) and fi...