Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.3 - Series - Exercise Set - Page 652: 48

Answer

In comparing the 2 jobs, Job B will pay more (by $\$3000$) over the next 5 years.

Work Step by Step

For Job A and B, an arithmetic sequence can be used to model each of the respective situation. For Job A, with $a_{1} = \$30000$ and $d = \$1200$, the general term is $a_{n} = 30000 + (n - 1)(1200)$. The partial sums of Job A over the next 5 years will be $\sum\limits_{n=1}^5 a_{n} = \sum\limits_{n=1}^5 30000 + (n - 1)(1200) = 30000 + 31200 + 32400 + 33600 + 34800 = \$162000$ While for Job B, with $a_{1} = \$28000$ and $d = \$2500$, the general term is $a_{n} = 28000 + (n - 1)(2500)$. The partial sums of Job B over the next 5 years will be $\sum\limits_{n=1}^5 a_{n} = \sum\limits_{n=1}^5 28000 + (n - 1)(2500) = 28000 + 30500 + 33000 + 35500 + 38000 = \$165000$ In comparing the 2 jobs, Job B will pay more (by $\$3000$) over the next 5 years.
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