Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1074: 64

$ a_2=-6$ and $ a_3=18 $

Here, we have $ a_1=2$ and $ a_2=a_1 r= 2r ;\\ a_3=a_1 r^2= 2r^2 ;\\ a_4=a_1 r^3= 2r^3=-54$ Now, $\dfrac{a_4}{a_1}=\dfrac{2r^3}{2}$ $ r^3=-27 \implies r=-3$ Now, $ a_2=a_1 r= 2(-3)=-6 ;\\ a_3=a_1 r^2= 2(-3)^2=18 $ Hence, $ a_2=-6$ and $ a_3=18 $