Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Chapter Test - Page 860: 2


$$\displaystyle a_1=4\\ a_2=14 \\ a_3=44 \\a_4=134 \\ a_5= 404$$

Work Step by Step

We are given that $a_n=3a_{n-1}+2$ and $a_1=4$. In order to determine the remaining values, we will have to substitute $n=2,3,4,5$ into the given sequence: $$\displaystyle a_2=3a_1+2=(3)(4)+2=14 \\ a_3=3 a_2+3=(3) (14)+2=44 \\a_4=3 a_3+2=(3)(44)+2=134 \\ a_5=3a_4+2=(3)(134)+2=404$$
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