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: 64


$a.\quad 42$ $b.\quad 2130$

Work Step by Step

The number of bricks is described as $\left\{\begin{array}{l} a_{1}=100\\ a_{n}=a_{n-1}-2 \end{array}\right.$, an arithmetic sequence with common difference $d=-2$. $a.$ The n-th term is $a_{n}=a_{1}+(n-1)d$, so the thirtieth is $a_{30}=100-2(29)=42$ $b.$ The sum $S_{n}$ of the first $n$ terms of $\left\{a_{n}\right\}$: $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ $S_{30}=\displaystyle \frac{30}{2}(100+42)=15(142)=2130$
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