If ( a, b, c ) are three consecutive terms of an ( A P ) and ( x, y, z ) are three consecutive terms of a G.P., then thevalue of ( X^ b-c , Y^ c-a , Z^ a-b ) is

Step-by-step solution

Given that, a , b , c are in A.P. and x , y , z are in G.P. Let d be the common difference between A.P. consecutive terms. So, b-a=c-b=d, c-a=2 d Now, ^ b-c y^ c-a z^ a-b =x^ -d y^ 2 d z^ -d =(x z)^ -d (y² )^ -d Since, x z=y² then (x z)^ -d (x z)^ d =1