Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 795: 46

$a_5=-\frac{\sqrt 2}{2}$

$a_n=a_1r^{n-1}$ $r=\frac{a_3}{a_2}$ $r=\frac{-\sqrt 2}{2}$ $a_5=a_1r^4$ $a_3=a_1r^2$ $\frac{a_5}{a_3}=\frac{a_1r^4}{a_1r^2}=r^2$ $a_5=a_3r^2=-\sqrt 2(\frac{-\sqrt 2}{2})^2=-\sqrt 2·\frac{2}{4}=-\frac{\sqrt 2}{2}$