AQA C2 2015 June — Question 5

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2015
SessionJune
TopicSequences and series, recurrence and convergence

5 The \(n\)th term of a sequence is \(u _ { n }\).
The sequence is defined by \(u _ { n + 1 } = p u _ { n } + q\), where \(p\) and \(q\) are constants.
The second term of the sequence is 160 . The third term of the sequence is 132 .
The limit of \(u _ { n }\) as \(n\) tends to infinity is 20 .
  1. Find the value of \(p\) and the value of \(q\).
  2. Hence find the value of the first term of the sequence.