ForthisproblemconsidertheAverageproblemstatedbelow. Average

Input: Output:

of n

integers A $=($a$1,$a$2,...,$an$).$

$1$ Xn m$=$ ai

A sequence

m in Q such that

n i$=1$

a$)$Using pseudocode state an algorithm that solves the Average problem using a

loop.

b$)$Identifytheloopinvariantfortheloopinyouralgorithmthatwillhelpyouprove your algorithm is correct. That is$,$ state the loop invariant as a proposition of the kind $$After iteration i of the loop...".

c$)$Usinginductionprovethatyourloopinvariantholdsforeachiterationi$.$

d$)$Usingtheloopinvariantshowthatyouralgorithmiscorrect$.$