College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding: 47

Answer

The first five terms are: $a_1= \sqrt2$ $a_2 = \sqrt{2+\sqrt2}$ $a_3 = \sqrt{2+\sqrt{2+\sqrt2}}$ $a_4 = \sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}$ $a_5= \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}}$

Work Step by Step

Use the given recursive formula to find the next four terms: $a_1= \sqrt2$ $a_2 = \sqrt{2+a_1} = \sqrt{2+\sqrt2}$ $a_3 = \sqrt{2+a_2} = \sqrt{2+\sqrt{2+\sqrt2}}$ $a_4 = \sqrt{2+a_3} = \sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}$ $a_5= \sqrt{2+a_4} = \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt2}}}}$
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