Explanation Concept: A sequence in which each term differs from the previous term by a constant amount d , the sequence is arithmetic sequence and the next term is calculated by the formula, a n = a n − 1 + d …… (1) Given: Job A offers annual starting salary of $30,000 with guaranteed annual raises of $1200 for next four years and Job B offers annual starting salary of $28,000 with guaranteed annual raises of $2500 for next four years. Calculation: As job A has annual starting salary of $30,000, this means the first term is a 1 = 30 , 000 and the common difference is d = 1200 . Substitute 2 for n , 1200 for d in equation (1) to calculate the second term. a 2 = a 2 − 1 + 1200 = a 1 + 1200 Substitute 30,000 for a 1 in the above equation. a 2 = 30 , 000 + 1200 = 31 , 200 Substitute 3 for n , 1200 for d in equation (1) to calculate the third term. a 3 = a 3 − 1 + 1200 = a 2 + 1200 Substitute 31,200 for a 2 in above equation. a 3 = 31 , 200 + 1200 = 32 , 400 Substitute 4 for n , 1200 for d in equation (1) to calculate the fourth term. a 4 = a 4 − 1 + 1200 = a 3 + 1200 Substitute 32,400 for a 3 in above equation. a 4 = 32 , 400 + 1200 = 33 , 600 Substitute 5 for n , 1200 for d in equation (1) to calculate the fifth term. a 5 = a 5 − 1 + 1200 = a 4 + 1200 Substitute 33,600 for a 4 in above equation. a 5 = 33 , 600 + 1200 = 34 , 800 The formula to calculate the sum of the sequences is, S n = ∑ i = 1 n a i …… (2) Substitute 5 for n in equation (2) to calculate the fifth sum. S 5 = ∑ i = 1 5 a i = a 1 + a 2 + a 3 + a 4 + a 5 = 30 , 000 + 31 , 200 + 32 , 400 + 33 , 600 + 34 , 800 = 1 , 62 , 000 As job B has annual starting salary of $28,000, this means the first term is b 1 = 28 , 000 and the common difference is d = 2500

7th Edition

ISBN: 9780135835357

Author: Pearson

Publisher: PEARSON

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Question

Chapter 11.3, Problem 48E

To determine

The job that pays more money over the next five years.

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Chapter 11.3, Problem 47E

Chapter 11.3, Problem 49E

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Chapter 11 Solutions

MML 18 WEEK SAC INTERMEDIATE ALGEBRA

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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