College Algebra (10th Edition)

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

Chapter 9 - Section 9.2 - Arithmetic Sequences - 9.2 Assess Your Understanding - Page 655: 66

Answer

$401.5$ inches (33.46 ft)

Work Step by Step

The rung length in inches forms an arithmetic sequence, with $a_{1}=49, d=-2.5,$ and $a_{n}=24$ The nth term is $a_{n}=a_{1}+(n-1)d$ $\quad 24=49+(n-1)(-2.5)\qquad$ ... solve for n $-25=-2.5(n-1)$ $10=n-1$ $11=n$ There are 11 rungs. $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ The sum of 11 rung lenths is $S_{11}=\displaystyle \frac{11}{2}(49+24)=401.5$ inches (33.46 ft)
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