Question 1 - A-Level Maths

Use mathematical induction to prove that $4 ^ { n } + 2$ is divisible by 6 for all positive integers $n$.
Solve the equation $2 z + i \bar { z } = \frac { - 1 + 7 i } { 2 + i }$.
1. Give your answer in Cartesian form
2. Give your answer in modulus-argument form.
3. Find an expression, in terms of $n$, for the sum of the first $n$ terms of the series
$$1.2 .4 + 2.3 .5 + 3.4 .6 + \ldots + n ( n + 1 ) ( n + 3 ) + \ldots$$ Express your answer as a product of linear factors.