2025 IGCSE Additional Mathematics May/June 0606/23 Q9

12 marks

The 1st term of an arithmetic progression is 9.
The last term of this progression is 159.
The sum of all the terms is 2604.
The 12th term of this arithmetic progression is the 1st term of a geometric progression.
The 8th term of this arithmetic progression is the 2nd term of the geometric progression.
Find the sum of the first 6 terms of the geometric progression.[7]
A different geometric progression has 1st term \(\sin\theta\).
The common ratio of this progression is \(\cos\theta\) where \(45^\circ\le\theta\le135^\circ\).
1. Show that this progression has a sum to infinity.[1]
2. Show that this sum to infinity can be written as \(\operatorname{cosec}\theta+\cot\theta\).[4]

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Answer:(a) \(183\) (3 significant figures). (b)(i) Shown. (ii) Shown.

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