Algebra 2 (1st Edition)

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

Chapter 12 Sequences and Series - 12.5 Use Recursive Rules with Sequences and Functions - Guided Practice for Examples 1 and 2 - Page 828: 5


$\left\{\begin{array}{l} a_{1}=2\\ a_{n}=7a_{n-1} \end{array}\right.$

Work Step by Step

Note that $\left\{\begin{array}{l} 14=2\times 7\\ 98=14\times 7\\ 686=98\times 7\\ 4802=686\times 7 \end{array}\right.\Rightarrow\quad a_{n}=7a_{n-1}$ for $n\geq 2$ (A geometric sequence is such that $a_{n}=r\cdot a_{n-1}$). For a recursive rule, we give the information about the first term, and a rule on how to obtain the next term from the preceding: $\left\{\begin{array}{l} a_{1}=2\\ a_{n}=7a_{n-1} \end{array}\right.$
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