CAIE P1 2019 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionNovember
TopicGeometric Sequences and Series

9 The first, second and third terms of a geometric progression are \(3 k , 5 k - 6\) and \(6 k - 4\), respectively.
  1. Show that \(k\) satisfies the equation \(7 k ^ { 2 } - 48 k + 36 = 0\).
  2. Find, showing all necessary working, the exact values of the common ratio corresponding to each of the possible values of \(k\).
  3. One of these ratios gives a progression which is convergent. Find the sum to infinity.