College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 7 - Section 7.1 - Sequences and Series - 7.1 Exercises - Page 635: 23

Answer

$a_1=-2 ,a_2=1 ,a_3=4 ,a_4=7$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the first four terms of the given sequence \begin{array}{l}\require{cancel} a_1=-2 \\\\ a_n=a_{n-1}+3, \text{ if }n\gt1 ,\end{array} use the given value for $a_1.$ Then use substitution to get the next $3$ terms. $\bf{\text{Solution Details:}}$ Using the value of $a_1$ and $n=2,$ the second term is \begin{array}{l}\require{cancel} a_2=a_{2-1}+3 \\\\ a_2=a_{1}+3 \\\\ a_2=-2+3 \\\\ a_2=1 .\end{array} Using the value of $a_2$ and $n=3,$ the third term is \begin{array}{l}\require{cancel} a_3=a_{3-1}+3 \\\\ a_3=a_{2}+3 \\\\ a_3=1+3 \\\\ a_3=4 .\end{array} Using the value of $a_3$ and $n=4,$ the fourth term is \begin{array}{l}\require{cancel} a_4=a_{4-1}+3 \\\\ a_4=a_{3}+3 \\\\ a_4=4+3 \\\\ a_4=7 .\end{array} Hence, the first four terms are $ a_1=-2 ,a_2=1 ,a_3=4 ,a_4=7 .$
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