Edexcel FP1 — Question 8

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

8. For \(n \in \mathbb { Z } ^ { + }\)prove that
  1. \(2 ^ { 3 n + 2 } + 5 ^ { n + 1 }\) is divisible by 3 ,
  2. \(\left( \begin{array} { r r } - 2 & - 1
    9 & 4 \end{array} \right) ^ { n } = \left( \begin{array} { c c } 1 - 3 n & - n
    9 n & 3 n + 1 \end{array} \right)\).