College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding - Page 666: 95

Answer

$1.845\times 10^{19}$ grains.

Work Step by Step

$a_{1}=1$ $a_{2}=1\cdot 2$ $a_{3}=1\cdot 2^{2}$ $a_{4}=1\cdot 2^{3}....$ a geometric sequence with $a_{1}=1,\quad r=2,\quad n=64.$ The sum $S_{n}$ of the first $n$ terms is $S_{n}=\displaystyle \sum_{k=1}^{n}a_{1}r^{k-1}=a_{1}\cdot\frac{1-r^{n}}{1-r}$ $S_{64}=1\displaystyle \frac{1-2^{64}}{1-2}=\frac{1-2^{64}}{-1}=2^{64}-1\approx 1.845\times 10^{19}$ $1.845\times 10^{19}$ grains. Say that there are 10,000 grains in a kilogram, there would be $10^{7}$ grains in a metric ton. A semi trailer truck can haul say, 50 tons.... You would need about $3.69\times 10^{10} $semitrailer truckloads.... $36,900,000,000 $ trucks.... It is quite possible that this is more wheat than has ever been grown on earth.
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