Q$2.[8]$ Write a pseudocode $($algorithm$)$ for a program named "AddFour&Sum$($A$)"$ that adds $4$

to each element in an integer array, A$,$ and sums all the elements using recursion. Try to make it

as efficient as possible in terms of number of assignments and comparisons.

Assume you have a built$-$in function or method RemoveFirstElement $(A)$ that takes in an integer

array $A$ as input, and returns the tail, which means the array A without the first element in it$.$

RemoveFirstElement$([$Single Item$])$ returns an empty array $[].$ Assume RemoveFirstElement$($A$)$

always takes $1$ assignment operation to run.

For Example: if $A=\left[\begin{array}{ccc}10& 20& 30\end{array}\right]$ then AddFour$\frac{\text{\&}}{S}um(A)$ should return $(10+4)+(20+4)+(30+4)=72$

a$)$ Write the recurrence relation counting assignments and comparisons only.

b$)$ Solve the recurrence relation using top$-$down substitution method.