This question is concerned with the design and analysis of recursive algorithms.

You are given a problem statement as shown below. This problem is concerned

with performing calculations on a sequence $$ of real numbers. Whilst this could

be done using a conventional loop$-$based approach, your answer must be

developed using a recursive algorithm. No marks will be given if your answer

uses loops.

$(1,...,)$ such that $>1$

Input: A sequence of real values $=(1,...,).$

Output:, A $2-$tuple $(,)$ containing the average $()$ of all the

values and the product $()$ of all the values of the elements in $.$

Your recursive algorithm should use a single recursive structure to find the

average and product values, and should not use two separate instances of a

recursive design. You should not employ any global variables.