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: 68


$30$ rows

Work Step by Step

The number of seats forms an arithmetic sequence, with $a_{1}=10,d=4,S_{n}=2040$ The sum $S_{n}$ of the first $n$ terms of $\left\{a_{n}\right\}$: $S_{n}=\displaystyle \frac{n}{2}\left[2a_{1}+(n-1)d\right]$ ... which we solve for n $2040=\displaystyle \frac{n}{2}[2(10)+(n-1)4]$ $4080=n[20+4n-4]$ $4080=4n^{2}+16n$ $4n^{2}+16n-4080=0$ $n^{2}+4n-1020=0$ ...use the quadratic formula $n=\displaystyle \frac{-4\pm\sqrt{16-4(1)(-1020)}}{2(1)}$ ... discard the negative solution $n=\displaystyle \frac{-4+64}{2}=30$
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