OCR FP1 2007 January — Question 6

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJanuary
TopicProof by induction

6 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by \(u _ { n } = n ^ { 2 } + 3 n\), for all positive integers \(n\).
  1. Show that \(u _ { n + 1 } - u _ { n } = 2 n + 4\).
  2. Hence prove by induction that each term of the sequence is divisible by 2 .