Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises: 39

Answer

*All decimal answers are rounded $a_1 = 54.45$ $a_2 = 54.95$ $a_3 = 54.99$ $a_4 = 54.999$ Converges; The limit of the sequence is $55$.

Work Step by Step

$a_{n+1} = \frac{a_n}{11} + 50$; $a_0 = 50$ *All decimal answers are rounded $a_1 = \frac{a_0}{11} + 50 = 54.45$ $a_2 = \frac{a_1}{11} + 50 = 54.95$ $a_3= \frac{a_2}{11} + 50 = 54.99$ $a_4 = \frac{a_3}{11} + 50 = 54.999$ Converges and approaches $55$. The terms of the sequence seems to get closer and closer to $55$.
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