Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - Chapter Review - Review Exercises - Page 839: 18

Answer

$10^{-10}.$

Work Step by Step

We know that $a_n=a_1r^{n-1}.$ where $d$=common ratio and $a_1$= the first term Here $a_1=1$ and $r=\frac{a_2}{a_1}=\dfrac{\frac{1}{10}}{1}=\frac{1}{10}$ Hence, here we have $a_n=1(\frac{1}{10})^{n-1}.$ Therefore $a_{11}=1(\frac{1}{10})^{11-1}\\=\frac{1}{10^{10}}=10^{-10}.$
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