Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.3 Geometric Sequences and Series - 11.3 Exercises: 14

Answer

$a)A_{18}=0.01\times 2^{18-1}=1310.72\$ $ $b)S_{18}=0.01\times \left( 2^{18}-1\right) =2621.43\$ $

Work Step by Step

Amount earned on the indicated day can be calculated with using simple geometric sequence formula $A_{n}=0.01\times 2^{n-1}$ And the total amount earned will be $ S_{n}=\dfrac {A_{1}\left( 1-r^{n}\right) }{1-r}=\dfrac {0.01\times \left( 1-2^{n}\right) }{1-2}=0.01\left( 2^{n}-1\right) $ $a)A_{18}=0.01\times 2^{18-1}=1310.72\$ $ $b)S_{18}=0.01\times \left( 2^{18}-1\right) =2621.43\$ $
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