Explanation Concept: A. The n th term of any geometric sequence with common ratio r and first term a 1 is given by the formula a n = a 1 r n − 1 . B. The partial sum S n of first n terms of a geometric sequence with common ratio r ≠ 1 and first term a 1 is given by the formula S n = a 1 ( 1 − r n ) 1 − r . Given: The earnings of frozen yogurt store owner in the first year are $20,000 and these earning increases by 15% in subsequent years. Calculation: The earnings increase by 15% each year. Earnings in second year = 20 , 000 + 15 % of 20 , 000 = 20 , 000 + 15 100 ( 20 , 000 ) = 23 , 000 Earnings in third year increase by 15% over the earnings in second year. Earnings in third year = 23 , 000 + 15 % of 23 , 000 = 23 , 000 + 15 100 ( 23 , 000 ) = 23 , 000 + 3450 = 26 , 450 And so on. These earnings form a sequence of the form 20000 , 23000 , 26450 , ⋯ . Check whether the given sequence is arithmetic or geometric. In any arithmetic sequence, the difference between the consecutive terms remains constant and the difference thus obtained is known as common difference. To check that the given sequence is arithmetic, find the difference between the consecutive terms. Subtract first term of the sequence from the second term. Second term − First term = 23000 − 20000 = 3000 Subtract second term of the sequence from the third term. Third term − Second term = 26450 − 23000 = 3450 The difference between the consecutive terms is not constant so the series is not arithmetic. In any geometric sequence, the ratio between any two consecutive terms remains constant. This ratio thus obtained is known as common ratio. To check that the given sequence is geometric, find the ratio between the consecutive terms. Calculate the ratio between the first term of the sequence and the second term. Second term First term = 23000 20000 = 1

7th Edition

ISBN: 9780134196176

Author: Elayn Martin-Gay

Publisher: PEARSON

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Question

Chapter 11.CR, Problem 59CR

To determine

The earning in fourth year and the total earnings in first four years, each rounded to nearest dollar.

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Chapter 11.CR, Problem 58CR

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Chapter 11 Solutions

Intermediate Algebra (7th Edition)

Ch. 11.1 - Prob. 1P Ch. 11.1 - Prob. 2P Ch. 11.1 - Prob. 3P Ch. 11.1 - Prob. 4P Ch. 11.1 - Prob. 1VRVC Ch. 11.1 - Prob. 2VRVC Ch. 11.1 - Prob. 3VRVC Ch. 11.1 - Prob. 4VRVC Ch. 11.1 - Prob. 5VRVC Ch. 11.1 - Prob. 6VRVC

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