Edexcel FP1 2009 June — Question 8

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJune
TopicProof by induction

8. Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\),
  1. \(\mathrm { f } ( n ) = 5 ^ { n } + 8 n + 3\) is divisible by 4 ,
  2. \(\left( \begin{array} { l l } 3 & - 2
    2 & - 1 \end{array} \right) ^ { n } = \left( \begin{array} { l r } 2 n + 1 & - 2 n
    2 n & 1 - 2 n \end{array} \right)\)