Arithmetic and Geometric Sequences

1. a , x1 , x2 , b and a , y1 , y2 , y3 , b are two geometric sequences
x1 = ar, x2 = ar^2 and b = ar^3
y1 = ak, y2 = ak^2 and y3 = ak^3, b = ak^4, where r and k are non-zero numbers.
x1x1/(y1y2y3) = a^2r^3/(a^3 k^6)
= a*ar^3/[(ak)^2(ak^4)]
= ab/(ak)^2(b)
= 1/ak^2
= 1/a^0.5(ak^4)^(0.5)
=1/(ab)^0.5
= (ab)^(-0.5)
The answer is D.
2. Let a be the first term and r be the common ratio of the geometric sequence.
a+ar+ar^2 = (19/27)*a/(1-r)
(1+r+r^2)(1-r) = 19/27
1+r+r^2 - r-r^2-r^3 = 19/27
8/27 - r^3 = 0
r^3 = 8/27 = (2/3)^3
r = 2/3
The answer is B.