College Algebra (11th Edition)

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

Chapter 7 - Section 7.2 - Arithmetic Sequences and Series - 7.2 Exercises: 11

Answer

$10+\sqrt{7}, 10, 10-\sqrt{7}, 10-2\sqrt{7}, 10-3\sqrt{7}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the first $5$ terms, solve first the common difference. Then keep adding the common difference to the given second term. $\bf{\text{Solution Details:}}$ The common difference is the difference between a term and the term before it. Hence, the common difference, $d,$ is \begin{array}{l}\require{cancel} d=a_2-a_1 \\\\ d=10-(10+\sqrt{7}) \\\\ d=10-10-\sqrt{7} \\\\ d=-\sqrt{7} ,\end{array} Adding the common difference, the third term is \begin{array}{l}\require{cancel} a_3=a_2+d \\\\ a_3=10-\sqrt{7} ,\end{array} the fourth term is \begin{array}{l}\require{cancel} a_4=a_3+d \\\\ a_4=10-\sqrt{7}-\sqrt{7} \\\\ a_4=10-2\sqrt{7} ,\end{array} and the fifth term is \begin{array}{l}\require{cancel} a_5=a_4+d \\\\ a_5=10-2\sqrt{7}-\sqrt{7} \\\\ a_5=10-3\sqrt{7} ,\end{array} Hence, the first $5$ terms are $ 10+\sqrt{7}, 10, 10-\sqrt{7}, 10-2\sqrt{7}, 10-3\sqrt{7} .$
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