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: 25


$a_1=1 ,a_2=1 ,a_3=2 ,a_4=3$

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=1 \\\\ a_2=1 \\\\ a_n=a_{n-1}+a_{n-2}, \text{ if }n\ge3 ,\end{array} use the given value for $a_1.$ Then use substitution to get the next $3$ terms. $\bf{\text{Solution Details:}}$ Using the values of $a_1,a_2,$ and $n=3,$ the third term is \begin{array}{l}\require{cancel} a_3=a_{3-1}+a_{3-2} \\\\ a_3=a_{2}+a_{1} \\\\ a_3=1+1 \\\\ a_3=2 .\end{array} Using the values of $a_2,a_3$ and $n=4,$ the fourth term is \begin{array}{l}\require{cancel} a_4=a_{4-1}+a_{4-2} \\\\ a_4=a_{3}+a_{2} \\\\ a_4=2+1 \\\\ a_4=3 .\end{array} Hence, the first four terms are $ a_1=1 ,a_2=1 ,a_3=2 ,a_4=3 .$
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