CAIE P1 2024 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionJune
TopicGeometric Sequences and Series

10 The geometric progression \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) has first term 2 and common ratio \(r\) where \(r > 0\). It is given that \(\frac { 9 } { 2 } a _ { 5 } + 7 a _ { 3 } = 8\).
  1. Find the value of \(r\).
  2. Find the sum of the first 20 terms of the geometric progression. Give your answer correct to 4 significant figures.
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  3. Find the sum to infinity of the progression \(a _ { 2 } , a _ { 5 } , a _ { 8 } , \ldots\).