SPS SPS SM 2024 October — Question 10

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

10. The first three terms of a geometric sequence are $$u _ { 1 } = 3 k + 4 \quad u _ { 2 } = 12 - 3 k \quad u _ { 3 } = k + 16$$ where \(k\) is a constant. Given that the sequence converges,
  1. Find the value of k , giving a reason for your answer.
  2. Find the value of \(\sum _ { r = 2 } ^ { \infty } u _ { r }\)