题目

Problem

A geometric progression has first term $a$ and common ratio $\cos\theta$ , where $0<\theta<\frac{1}{2}\pi$ . It is given that the second term is 8 and the fifth term is $\frac{1}{8}$ .

(a) Find the value of $\theta$ . Give your answer correct to 3 significant figures.

[3]

(b) Find the exact value of the sum to infinity.

[2]

题目中文翻译

一个等比数列的首项为 $a$ ，公比为 $\cos\theta$ ，其中 $0<\theta<\frac{1}{2}\pi$ 。已知第二项为 8，第五项为 $\frac{1}{8}$ 。

(a) 求 $\theta$ 的值，答案精确到 3 位有效数字。

(b) 求无穷和的精确值。

CIE 9709 2025 Nov Paper 11 Q2

题目

解答