The correct option is D x,y,z are in AP
x,y,z are in GP.
⇒y2=xz
α,β,γ are in AP.
⇒2β=α+γ
⇒tan(2β)=tan(α+γ)
⇒2tanβ1−tan2β=tanα+tanγ1−tanαtanγ
⇒2y1−y2=x+z1−xz
⇒2y=x+z and y≠1
⇒x,y,z are in AP.
Since, x,y,z are in AP and GP,
x,y,z is a constant sequence.