Given the sequence defined with the recurrence relation:
Given the sequence defined with the recurrence relation:
$$ \begin{array}{l} a_{0}=2 \\ a_{k}=4 a_{k-1}+5 \text { for } n \geq 0 \end{array} $$
A. (3 marks) Terms of Sequence Calculate \(a_{1}, a_{2}, a_{3}\) Keep your intermediate answers as you will need them in the next questions
B. ( 7 marks) Iteration Using iteration, solve the recurrence relation when \(n \geq 0\) (i.e. find an analytic formula for \(a_{n}\) ). Simplify your answer as much as possible, showing your work. In particular, your final answer should not contain \(\sum\) and \(\prod\). You must show your work to get full marks.
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