Sequence and series

Q1 ans is AP


@ashishdeosingh
How did 2nd last step came ?I can't understand.

@nishantthakre by cross multiplying the third last step...(a+b)(ab)=a²b²

@ashishdeosingh sir, I just want to know is there any way to manipulate x,y,z which are in H.P to form that question.....or just by checking option by taking first it as A.P then other to verify.....?

@username
you can start from my last step and work in reverse.

@ashishdeosingh ohh yaa, thanks sir