Respuesta :
Using a geometric sequence, it is found that it executes 117,440,512 operations when it is run with an input of size 24.
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
- Since the algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k − 1, the common ratio is q = 2.
- When the algorithm is run with an input of size 1, it executes seven operations, hence the first term is [tex]a_1 = 7[/tex].
Then, for a input size of n, the number of operations is given by:
[tex]a_N = 7(2)^n[/tex]
Then, for a input size of 24:
[tex]a_{24} = 7 \times 2^{24} = 117440512[/tex]
It executes 117,440,512 operations when it is run with an input of size 24.
More can be learned about geometric sequences at https://brainly.com/question/11847927
