College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Chapter 8 Review - Exercises - Page 639: 10


$a_1=\sqrt{3}=3^{1/2}$ $a_2=3^{3/4}$ $a_{3}=3^{7/8}$ $a_{4}=3^{15/16}$ $a_{5}=3^{31/32}$ $a_6=3^{63/64}$ $a_7=3^{127/128}$

Work Step by Step

We are given: $a_{n}=\sqrt{3a_{n-1}}$ and $a_1=\sqrt{3}$ We evaluate: $a_2=\sqrt{3a_1}=\sqrt{3\sqrt{3}}=(3*3^{1/2})^{1/2}=3^{3/4}$ $a_{3}=\sqrt{3a_{2}}=\sqrt{3^1*3^{3/4}}=\sqrt{3^{7/4}}=3^{7/8}$ $a_{4}=\sqrt{3a_{3}}=\sqrt{3^1*3^{7/8}}=\sqrt{3^{15/8}}=3^{15/16}$ $a_{5}=\sqrt{3a_4}=\sqrt{3^1*3^{15/16}}=\sqrt{3^{31/16}}=3^{31/32}$ $a_6=\sqrt{3a_{5}}=\sqrt{3^1*3^{31/32}}=\sqrt{3^{63/32}}=3^{63/64}$ $a_7=\sqrt{3a_6}=\sqrt{3^1*3^{63/64}}=\sqrt{3^{127/64}}=3^{127/128}$
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