A certain computer 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 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 28? For each integer n 2 1, let s, be the number of operations the algorithm executes when it is run with an input of size n. Then s, = 7 v and for each integer k 2 1. Therefore, s,, s,, S2, is a geometric sequence V with constant final value x which is 2 . So, for S = every integern2 0, s, = 7 It follows that for an input of size 28, the number of operations executed by the algorithm is s27 which equals 939524096

A certain computer 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 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 28? For each integer n 2 1, let s, be the number of operations the algorithm executes when it is run with an input of size n. Then s, = 7 v and for each integer k 2 1. Therefore, s,, s,, S2, is a geometric sequence V with constant final value x which is 2 . So, for S = every integern2 0, s, = 7 It follows that for an input of size 28, the number of operations executed by the algorithm is s27 which equals 939524096

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 52E

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