Chapter 11 - Section 11.2 - Arithmetic and Geometric Sequences - Exercise Set - Page 647: 45

$a_{6}= \dfrac{8}{81}$

Using $a_n=a_1r^{n-1}$ or the $n$th term of a geometric sequence, then, \begin{array}{l} a_{6}=24\left( \dfrac{1}{3} \right)^{6-1} \\\\ a_{6}=24\left( \dfrac{1}{243} \right) \\\\ a_{6}= \dfrac{8}{81} .\end{array}