Time Complexity

Question

hope(n){
if (n == 1)
G(n)
else
F() + hope(n/2);
}
What is the time complexity for the given function, if the function ‘G’ and function ‘F’ take O(1) and O(n) unit of time respectively.
My views: If we take the recursion in the form of "T(n) = T(n/2) + O(n)" then the answer is definitely O(n). But my understanding is still incomplete. If we don't consider that form mentioned above and imagine hope(n/2) being  recursively called, isn't F() being called 'log n'  times as well? Why can't the answer be O(nlogn) since F() (whose complexity is O(n)) is called 'log n' times?

Comments

@Warlock lord

yes F() is called logn times, but complexity of F() will not be O(n) in every call, it will also decrease with n.

it will go like-> n + n/2 + n/4 + n/8.........logn times = O(n)

what you are doing is -> n + n + n + n...........logn times = O(nlogn)  // this is incorrect

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yes understood :) thanks nitish