CAIE P1 2014 November — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionNovember
TopicGeometric Sequences and Series

4 Three geometric progressions, \(P , Q\) and \(R\), are such that their sums to infinity are the first three terms respectively of an arithmetic progression. Progression \(P\) is \(2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots\).
Progression \(Q\) is \(3,1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots\).
  1. Find the sum to infinity of progression \(R\).
  2. Given that the first term of \(R\) is 4 , find the sum of the first three terms of \(R\).