If `(a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0)` then show that a, b, c and d are in G.P.

Explanation

It is given that
`(a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx)=lamda`(say)
Now, `(a+bx)/(a-bx)=lamda/1=lamda`
or `((a+bx)-(a-bx))/((a+bx)+(a-bx))=(lamda-1)/(lamda+1)`
or `(bx)/a=(lamda-1)/(lamda+1)`
or `b/a=((lamda-1))/(x(lamda+1))`
Thus,a,b,c,d are in G.P.