Question

if a,b,and c,are in geometric progression then a-b divided by b-c is equal to

Answer 1

let a = xr
b = x
c =x/r

now, ( a - b) /( b - c) = ( xr- x)/( x -x/r)
=x( 1 - r)/(1- 1/r)x
= -x(r - 1)/x( r - 1)/r
=-r
but r = b/a = c/b
so, ( a - b)/( b -c) = -b/a = -c/b