SPS SPS SM Pure 2024 June — Question 12

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionJune
TopicGeometric Sequences and Series

  1. In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology or numerical methods are not acceptable. A geometric sequence has first term \(a\) and common ratio \(r\), where \(r > 0\)
Given that
  • the 3rd term is 20
  • the 5th term is 12.8
    1. show that \(r = 0.8\)
    2. Hence find the value of \(a\).
Given that the sum of the first \(n\) terms of this sequence is greater than 156
  • find the smallest possible value of \(n\).