Question :If $\displaystyle a^x = b^y = c^z$ and $\displaystyle b^2 = ac$ show that $\displaystyle 1/x,1/y,1/z $are in A.P?

The solution which i got here is as follows.(PFA)

i don't understand how $\displaystyle 2/y = 1/x + 1/z $ says it to be A.P.

if i am not wrong, a sequence is said to be in AP if the next number in the sequence differs from the previous number by a constant value D. So I'm confused with the solution.Will someone please explain?