If logy⁡x,logz⁡y,−15logx⁡z are in A.P., then

Let d be the common difference of the A.P.then,logy⁡x=1+d⇒x=y1+dlogz⁡y=1+2d⇒y=z1+2d and −15logx⁡z=1+3d⇒z=x−(1+3d)/15∴ x=y1+d=z(1+2d)(1+d) =x−(1+d)(1+2d)(1+3d)/15⇒ (1+d)(1+2d)(1+3d)=−15⇒ 6d3+11d2+6d+16=0⇒ (d+2)6d2−d+8=0⇒d=−2∴ x=y1+d=y−1,y=z1+2d=z−3 and x=z−3−1=z3.