Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 815: 59

Answer

24 terms

Work Step by Step

We are given the arithmetic sequence: $a_1=11$ $d=3$ $S_n=1092$ We determine $n$ solving the equation: $S_n=\dfrac{n(2a_1+(n-1)d)}{2}$ $1092=\dfrac{n(2(11)+(n-1)(3)}{2}$ $2(1092)=n(22+3n-3)$ $2184=n(3n+19)$ $3n^2+19n-2184=0$ $n=\dfrac{-19\pm\sqrt{19^2-4(3)(-2184)}}{2(3)}=\dfrac{-19\pm 163}{6}$ $n_1=\dfrac{-19-163}{6}=-\dfrac{182}{6}=-\dfrac{91}{3}$ $n_2=\dfrac{-19+163}{6}=\dfrac{144}{6}=24$ As $n$ must be a positive integer, the only solution is: $n=24$
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