Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - Guided Practice for Examples 2, 3, and 4 - Page 804: 4


$a_{n}=5n-9$ $a_{20}=91$

Work Step by Step

If the sequence is arithmetic, the general rule is $ a_{n}=a_{1}+(n-1)d\qquad$ (Our goal is to find $a_{1}$ and $d.)$ Use the given information $\left\{\begin{array}{lll} 26=a_{1}+(7-1)d & ... & (n=7)\\ 71=a_{1}+(16-1)d & ... & (n=6) \end{array}\right.\qquad$... simplify both equations $\left\{\begin{array}{ll} 26=a_{1}+6d & \\ 71=a_{1}+15d & \end{array}\right.\qquad$... subtract the first from the second equation $ 45=9d \qquad$... divide with 9 $5=d$ ... back-substitute into $26=a_{1}+6d$ $26=a_{1}+6(5)$ $26=a_{1}+30$ $-4=a_{1}$ So, the general rule is $a_{n}=-4+(n-1)(5)$ $a_{n}=-4+5n-9$ $a_{n}=5n-9$ The 20th term is $a_{20}=5(20)-9=91$
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