A sequence of integers is said to be an arithmetic progression if the difference of consecutive terms is constant. For example, $-3,0,3,6$ and $8,6,4,2$ are both arithmetic progressions.

You are given an arithmetic progression $A$ of size $n$ with one element missing! Design a

Divide and Conquering algorithm to find the missing element.

Example: for $A=[2,5,8,14]$ your output should be $11.$

You can assume the missing element is not at the beginning or the end.

A complete submission will include:

$($a$)$ describe your algorithm in words $($no pseudocode!$)$

$($b$)$ justify its correctness

$($c$)$ analyze and state its runtime. $[$Faster $($and correct$)$ in asymptotic Big O notation is worth

more credit.$]$