Explanation Given information: The expression is 1 3 + 2 3 + 1 + 4 3 + ⋅ ⋅ ⋅ + 33 . Concept used: Arithmetic sequenceis the sequence such that the difference of two consecutive terms is same. It can be represented as, a 1 , a 1 + d , a 1 + 2 d , a 1 + 3 d , ... , a 1 + ( n − 1 ) d Here, a 1 is the first term of the sequence and d is the common difference. The general formula for the nth term of the arithmetic sequence is, a n = a + ( n − 1 ) d ........ ( 1 ) The general formula for the nth partial sum of arithmetic sequence is, S n = n 2 ( a + a n ) ........ ( 2 ) Here, a n is the last term of an arithmetic sequence. Geometric sequence is the sequence such that the ratio of two consecutive terms is same. It can be represented as, a , a r , a r 2 , a r 3 , ... , a r n − 1 Here, a 1 is the first term of the sequence and r is the common ratio. The general formula for the n t h partial sum of geometric sequence a + a r + a r 2 + a r 3 + ⋅ ⋅ ⋅ + a r n − 1 is, S n = a ( 1 − r n ) 1 − r Here, r ≠ 1 Calculation: The given expression is 1 3 + 2 3 + 1 + 4 3 + ⋅ ⋅ ⋅ + 33 . Here, first term a 1 is 1 3 , second term a 2 is 2 3 , third term a 3 is 1 and last term a n is 33

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 8, Problem 52E

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Whether the expression 13+23+1+43+⋅⋅⋅+33 is a partial sum of an arithmetic or geometric sequence. Also, find the sum.

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Chapter 8, Problem 51E

Chapter 8, Problem 53E

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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? Find the first five terms of...Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Terms of an Arithmetic Sequence Determine the...Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55E Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.2 - Prob. 59E Ch. 8.2 - Partial Sums of an Arithmetic Sequence A partial...Ch. 8.2 - Partial Sums of an Arithmetic Sequence A partial...Ch. 8.2 - Prob. 62E Ch. 8.2 - Prob. 63E Ch. 8.2 - Prob. 64E Ch. 8.2 - Prob. 65E Ch. 8.2 - Prob. 66E Ch. 8.2 - Prob. 67E Ch. 8.2 - Prob. 68E Ch. 8.2 - Prob. 69E Ch. 8.2 - Prob. 70E Ch. 8.2 - Prob. 71E Ch. 8.2 - Prob. 72E Ch. 8.2 - Prob. 73E Ch. 8.2 - Prob. 74E Ch. 8.2 - Prob. 75E Ch. 8.2 - Prob. 76E Ch. 8.2 - Prob. 77E Ch. 8.2 - Prob. 78E Ch. 8.3 - A geometric sequence is a sequence in which the...Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - (a) The nth partial sum of a geometric sequence...Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - 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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 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Mortgage A couple can afford to make a monthly...Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Interest Rate An item at a department store is...Ch. 8.4 - Interest Rate A man purchases a $2000 diamond ring...Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - DISCOVR: Amortizing a Mortgage When they bought...Ch. 8.5 - Mathematical induction is a method of proving that...Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - Prob. 5E Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - Prob. 12E Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Proving a Statement Use mathematical induction to...Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Prob. 30E Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.6 - An algebraic expression of the form a+b, which...Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Prob. 24E Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Term of a Binomial Expansion Find the indicated...Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - 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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Whether the expression 1 3 + 2 3 + 1 + 4 3 + ⋅ ⋅ ⋅ + 33 is a partial sum of an arithmetic or geometric sequence. Also, find the sum.

Solution Summary: The author explains that the expression 13+fric2 3+1+ fcdot +33 is an arithmetic sequence and the sum is

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To find:

Whether the expression 13+23+1+43+⋅⋅⋅+33 is a partial sum of an arithmetic or geometric sequence. Also, find the sum.

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Chapter 8 Solutions

Whether the expression 1 3 + 2 3 + 1 + 4 3 + ⋅ ⋅ ⋅ + 33 is a partial sum of an arithmetic or geometric sequence. Also, find the sum.

Solution Summary: The author explains that the expression 13+fric2 3+1+ fcdot +33 is an arithmetic sequence and the sum is

Concept explainers

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To find: Whether the expression 13+23+1+43+⋅⋅⋅+33 is a partial sum of an arithmetic or geometric sequence. Also, find the sum.

Want to see the full answer?

Chapter 8 Solutions

To find:

Whether the expression 13+23+1+43+⋅⋅⋅+33 is a partial sum of an arithmetic or geometric sequence. Also, find the sum.