Explanation Given information: The total amount of drug in the bloodstream after the n th dose is, ∑ k = 1 n 50 ( 1 2 ) k − 1 Calculation: The total amount A of drug in the bloodstream after the n th dose is, A = ∑ k = 1 n 50 ( 1 2 ) k − 1 ....... (1) The amount of drug in the bloodstream after 10 days is calculated if 10 is substituted for n in equation (1). A = ∑ k = 1 10 50 ( 1 2 ) k − 1 ....... (2) The n th term of a geometric sequence is, a n = a r n − 1 ....... (3) Compare equation (3) with the equation (1) to obtain the common ratio r as, r = 1 2 Substitute 1 for k in equation (2) to obtain the first term a as, a = 50 ( 1 2 ) 1 − 1 = 50 ( 1 2 ) 0 = 50 ⋅ 1 a = 50 The number of terms in the geometric sequence is, n = 10 The sum of n terms of geometric sequence is, S n = a ( 1 − r n 1 − r ) To determine (b) To calculate: The sum of the series ∑ k = 1 ∞ 50 ( 1 2 ) k − 1 .

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Chapter 8.3, Problem 96E

To determine

(a)

To calculate:

The amount of drug in the bloodstream after 10 days.

To determine

(b)

To calculate:

The sum of the series ∑k=1∞50( 1 2 )k−1.

Expert Solution & Answer

Chapter 8 Solutions

College Algebra

Ch. 8.1 - A sequence is a function whose domain is...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Terms of a Sequence, Find the first four terms and...Ch. 8.1 - Prob. 6E Ch. 8.1 - Terms of a Sequence, Find the first four terms and...Ch. 8.1 - Terms of a Sequence, Find the first four terms and...Ch. 8.1 - Terms of a Sequence, Find the first four terms and...Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Recursive Sequences A sequence is defined...Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - nth term of a Sequence Find the nth term of a...Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - nth Partial Sum Find the first four partial sums...Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - Prob. 61E Ch. 8.1 - Prob. 62E Ch. 8.1 - Prob. 63E Ch. 8.1 - Prob. 64E Ch. 8.1 - Prob. 65E Ch. 8.1 - Sigma Notation Write the sum without using sigma...Ch. 8.1 - Prob. 67E Ch. 8.1 - Prob. 68E Ch. 8.1 - Prob. 69E Ch. 8.1 - Prob. 70E Ch. 8.1 - Prob. 71E Ch. 8.1 - Prob. 72E Ch. 8.1 - Prob. 73E Ch. 8.1 - Prob. 74E Ch. 8.1 - Prob. 75E Ch. 8.1 - Prob. 76E Ch. 8.1 - Prob. 77E Ch. 8.1 - Prob. 78E Ch. 8.1 - Population of a City A city was incorporate in...Ch. 8.1 - Prob. 80E Ch. 8.1 - Prob. 81E Ch. 8.1 - Prob. 82E Ch. 8.1 - Prob. 83E Ch. 8.1 - Prob. 84E Ch. 8.1 - Prob. 85E Ch. 8.1 - Prob. 86E Ch. 8.1 - Prob. 87E Ch. 8.1 - Prob. 88E Ch. 8.2 - An arithmetic sequence is a sequence in which the...Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Arithmetic Sequence? Find the first five terms of...Ch. 8.2 - Prob. 29E Ch. 8.2 - Arithmetic Sequence? 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Prob. 90E Ch. 8.3 - Mixing Coolant A truck radiator holds 5 gal and is...Ch. 8.3 - Musical Frequencies The frequencies of musical...Ch. 8.3 - Bouncing Ball A ball is dropped from a height of 9...Ch. 8.3 - Prob. 94E Ch. 8.3 - Prob. 95E Ch. 8.3 - Prob. 96E Ch. 8.3 - Prob. 97E Ch. 8.3 - Prob. 98E Ch. 8.3 - Prob. 99E Ch. 8.3 - Geometry A circular disk of radius R is cut out of...Ch. 8.3 - Geometry A yellow square of side I is divided into...Ch. 8.3 - Prob. 102E Ch. 8.3 - Prob. 103E Ch. 8.3 - Prob. 104E Ch. 8.4 - An annuity is a sum of money that is paid in...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Annuity Find the amount of an annuity that...Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Saving How much money should be invested every...Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Mortgage What is the monthly payment on a 30-year...Ch. 8.4 - Mortgage what is the monthly payment on a 30-year...Ch. 8.4 - 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Prob. 36E Ch. 8.6 - Term of a Binomial Expansion Find the indicated...Ch. 8.6 - Prob. 38E Ch. 8.6 - Prob. 39E Ch. 8.6 - Prob. 40E Ch. 8.6 - Prob. 41E Ch. 8.6 - Prob. 42E Ch. 8.6 - Prob. 43E Ch. 8.6 - Prob. 44E Ch. 8.6 - Prob. 45E Ch. 8.6 - Prob. 46E Ch. 8.6 - Prob. 47E Ch. 8.6 - Prob. 48E Ch. 8.6 - Prob. 49E Ch. 8.6 - Prob. 50E Ch. 8.6 - Prob. 51E Ch. 8.6 - Prob. 52E Ch. 8.6 - Prob. 53E Ch. 8.6 - Prob. 54E Ch. 8.6 - Prob. 55E Ch. 8.6 - Prob. 56E Ch. 8.6 - Prob. 57E Ch. 8.6 - Prob. 58E Ch. 8.6 - Prob. 59E Ch. 8 - Prob. 1CC Ch. 8 - Prob. 2CC Ch. 8 - Prob. 3CC Ch. 8 - Prob. 4CC Ch. 8 - Prob. 5CC Ch. 8 - Prob. 6CC Ch. 8 - Prob. 7CC Ch. 8 - Prob. 8CC Ch. 8 - Prob. 9CC Ch. 8 - Prob. 10CC Ch. 8 - Prob. 11CC Ch. 8 - Prob. 12CC Ch. 8 - Prob. 1E Ch. 8 - Prob. 2E Ch. 8 - Prob. 3E Ch. 8 - Prob. 4E Ch. 8 - Prob. 5E Ch. 8 - Prob. 6E Ch. 8 - Prob. 7E Ch. 8 - Prob. 8E Ch. 8 - Prob. 9E Ch. 8 - Prob. 10E Ch. 8 - Prob. 11E Ch. 8 - Prob. 12E Ch. 8 - Prob. 13E Ch. 8 - Prob. 14E Ch. 8 - Arithmetic or Geometric? The first four terms of a...Ch. 8 - Prob. 16E Ch. 8 - Prob. 17E Ch. 8 - Prob. 18E Ch. 8 - Prob. 19E Ch. 8 - Prob. 20E Ch. 8 - Prob. 21E Ch. 8 - Prob. 22E Ch. 8 - Prob. 23E Ch. 8 - Prob. 24E Ch. 8 - Prob. 25E Ch. 8 - Prob. 26E Ch. 8 - Prob. 27E Ch. 8 - Finding Terms of Arithmetic and Geometric...Ch. 8 - Salary A teacher makes $32,000 in his first year...Ch. 8 - SalaryA Colleague of the teacher in Exercise 29,...Ch. 8 - Prob. 31E Ch. 8 - Prob. 32E Ch. 8 - Prob. 33E Ch. 8 - Prob. 34E Ch. 8 - Prob. 35E Ch. 8 - Prob. 36E Ch. 8 - Prob. 37E Ch. 8 - Prob. 38E Ch. 8 - Prob. 39E Ch. 8 - Prob. 40E Ch. 8 - Prob. 41E Ch. 8 - Prob. 42E Ch. 8 - Prob. 43E Ch. 8 - Prob. 44E Ch. 8 - Prob. 45E Ch. 8 - Prob. 46E Ch. 8 - Prob. 47E Ch. 8 - Prob. 48E Ch. 8 - Prob. 49E Ch. 8 - Prob. 50E Ch. 8 - Prob. 51E Ch. 8 - Prob. 52E Ch. 8 - Prob. 53E Ch. 8 - Prob. 54E Ch. 8 - Prob. 55E Ch. 8 - Prob. 56E Ch. 8 - Prob. 57E Ch. 8 - Prob. 58E Ch. 8 - Prob. 59E Ch. 8 - Prob. 60E Ch. 8 - Prob. 61E Ch. 8 - Prob. 62E Ch. 8 - AncestorsA person has two parents, four...Ch. 8 - Prob. 64E Ch. 8 - Prob. 65E Ch. 8 - Prob. 66E Ch. 8 - Prob. 67E Ch. 8 - Prob. 68E Ch. 8 - Prob. 69E Ch. 8 - Prob. 70E Ch. 8 - Prob. 71E Ch. 8 - Prob. 72E Ch. 8 - Prob. 73E Ch. 8 - Prob. 74E Ch. 8 - Prob. 75E Ch. 8 - Prob. 76E Ch. 8 - Prob. 77E Ch. 8 - Prob. 78E Ch. 8 - Prob. 79E Ch. 8 - Prob. 80E Ch. 8 - Prob. 81E Ch. 8 - Prob. 82E Ch. 8 - Prob. 83E Ch. 8 - Prob. 1T Ch. 8 - Prob. 2T Ch. 8 - Prob. 3T Ch. 8 - Prob. 4T Ch. 8 - Prob. 5T Ch. 8 - Prob. 6T Ch. 8 - Prob. 7T Ch. 8 - Prob. 8T Ch. 8 - Prob. 9T Ch. 8 - Prob. 10T Ch. 8 - Prob. 11T Ch. 8 - Prob. 12T Ch. 8 - Prob. 13T Ch. 8 - Prob. 1P Ch. 8 - Fitness Progam Sheila decides to embark on a...Ch. 8 - Monthly Savings Program Alice opens a savings...Ch. 8 - Pollution A chemical plant discharges 2400 tons of...Ch. 8 - Prob. 5P Ch. 8 - Prob. 6P

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(a) To calculate: The amount of drug in the bloodstream after 10 days.

Solution Summary: The author calculates the amount of drug in the bloodstream after the nth dose.