Edexcel FP1 2011 June — Question 9

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
TopicProof by induction

9. Prove by induction, that for \(n \in \mathbb { Z } ^ { + }\),
  1. \(\left( \begin{array} { l l } 3 & 0
    6 & 1 \end{array} \right) ^ { n } = \left( \begin{array} { c c } 3 ^ { n } & 0
    3 \left( 3 ^ { n } - 1 \right) & 1 \end{array} \right)\),
  2. \(\mathrm { f } ( n ) = 7 ^ { 2 n - 1 } + 5\) is divisible by 12 .