Please answer fully
I am beginner for this
if a , b ,c are in AP x , y , z are in GP . Prove that (x^b/x^c)× (y^c/y^a)× (z^a/z^b)=1
x^a * x^b = x^c
so, x^b/x^c = 1/x^a
similarly, y^c/y^a = y^b
y/x = z/y
(x^b/x^c)× (y^c/y^a)× (z^a/z^b)
= 1/x^a * y^b * z^a/z^b
= (y/z)^b * (z/x)^a
= (x/y)^b * (y/x)^2a
= (x/y)^(b-2a)
Now, since b-a = c-b, 2b=a+c
b-2a = b-a + b-c
= 2b-(a+c)
= 0
(x/y)^0 = 1