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CIE 9709 2025 Nov Paper 15 Q2

A Level / CIE / P1

CIE 9709 2025 Nov Paper 15 Paper · Question 2

题目

Problem

A geometric progression has first term 3+423+4\sqrt{2} and second term 525-\sqrt{2}.

(a) Find the common ratio of the geometric progression. Give your answer in the form 2+p\sqrt{2}+p, where pp is an integer to be found.

[3]

(b) Find the sum to infinity of the geometric progression.

[2]
题目中文翻译

一个等比数列的第一项为 3+423+4\sqrt{2},第二项为 525-\sqrt{2}

(a) 求这个等比数列的公比。答案写成 2+p\sqrt{2}+p 的形式,其中 pp 是需要求出的整数。

(b) 求这个等比数列的无穷和。

解答