Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Problem Solving - Page 816: 61c

Answer

For company A and B we have $A: \$ 590,000; B: \$ 595,562$

Work Step by Step

Here, we have $a_1= 20,000$ and $b_1= 20,000$ We know that $a_n=a_1+(n-1)d$ Plug $d=1000$ And $r=1+0.04=1.04$ $a_{20}=20,000+(20-1) \times (1000)=39,000$ $S_{20}=\dfrac{20 \times (20,000+39000)}{2}=590,000$ The sum $T_n$ of the first n terms of the sequence $b_n$ can be found as: $T_n=\dfrac{20,000(1-1.04^{20})}{1-1.04} \approx 595,562$ Hence, for company A and B we have $A: \$ 590,000; B: \$ 595,562$
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