Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7 - Page 330: 129


On\[{{15}^{th}}\] day the person puts aside\[\$16,384\].

Work Step by Step

: The provided information can be modelled as a geometric progression with the following parameters: \[a=1,\,r=2,\,n=15\] The fifteenth term is, \[\begin{align} & {{a}_{n}}=a{{r}^{n-1}} \\ & {{a}_{15}}=1\times {{2}^{\left( 15-1 \right)}} \\ & ={{2}^{14}} \\ & =16384 \end{align}\] Hence, on\[{{15}^{th}}\] day the person puts aside\[\$16,384\].
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