
Hi Shubhangi
You can easily check with some numbers that it is not compulsory for a, b, c to follow either AP or GP.
For example, let's take x = 1, y = 2 and z = 4 such that x, y, z are in AP.
Now let a = 16, b = 4 and c = 2 such that a^{x} = b^{y} = c^{z} i.e. 16^{1} = 4^{2} = 2^{4}.
But you can easily see that 16, 4, 2 are neither in AP or GP.
Kamal Lohia
