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 - 12.5 Exercises - Skill Practice - Page 831: 42a

Answer

$5,18,9,30,15,48,24,12,6,3$

Work Step by Step

Calculate the first ten terms: $$\begin{align*} a_1&=5\\ a_2&=3(5)+3=18\\ a_3&=\dfrac{18}{2}=9\\ a_4&=3(9)+3=30\\ a_5&=\dfrac{30}{2}=15\\ a_6&=3(15)+3=48\\ a_7&=\dfrac{48}{2}=24\\ a_8&=\dfrac{24}{2}=12\\ a_9&=\dfrac{12}{2}=6\\ a_{10}&=\dfrac{6}{2}=3. \end{align*}$$ We notice that $a_{11}=3(3)+3=12$ and the sequence $12,6,3$ repeats indefinitely.
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