Question

if p,q,r are in A.P
and x, y,z are in G.P. then ​

Answer 1

Let d be the common difference of A.P. and R(

Not =0), the common ratio of G.P, then

q=p+d,r=p+2d and y=xR,z=xR2

So that q−r=−d,r−p=2d,p−q=−d

∴x q−r .y r−p .z p−q

=x −d .(xR) 2d .(xR 2 ) −d

=(x −d .x 2d .x −d )(R 2d .R −2d )

=(x −d+2d−d ).(R 2d−2d )

=x 0.R 0

=1×1=1