insert 6 g.m.s between 8/27 and -5 1/16.

Answer 1

the terms would be
8/27, (8/27)r, (8/27)r^2, (8/27)r^3, (8/27)r^4, (8/27)r^5, (8/27)r^6 , -81/6

(8/27)r / (8/27) = (-81/16) / ((8/27)r^5)

r^7 = (-81/16)(27/8)
r^7 = (-3)^7 / 2^7
r = -3/2

I will let you find the terms to be inserted

Answer 2

-4/9,2/3,-1,3/2-9/4,27/8