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: 59



Work Step by Step

The sum $S_{n}$ of the first $n$ terms of $\left\{a_{n}\right\}$: $S_{n}=\displaystyle \frac{n}{2}\left[2a_{1}+(n-1)d\right]$ $ 1092=\displaystyle \frac{n}{2}\left[2(11)+3(n-1)\right]\quad$ ... solve for n $2194=n[22+3n-3]$ $2194=19n+3n^{2}$ $3n^{2}+19n-2184=0$ ... use the quadratic formula $n=\displaystyle \frac{-19\pm\sqrt{19^{2}-4(3)(-2184)}}{2(3)}$ ... discard the negative n.... $n=\displaystyle \frac{-19+163}{6}=24$
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