Write. a JavaFx program with explanation of code for the following:- ( NO ERRORS )

First, given a sorted integer list (e.g., {1, 3, 5, 7, ..., 99}), implement a linear time O(n) search algorithm for obtaining the index of the key 77. Then implement a O(logn) search algorithm performing the same task. Second, design an O(n) time algorithm for computing the sum of numbers from n1 to n2 (n1 < n2, for example n1=1 and n2=100) and then design an O(1) algorithm for performing the same task.

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