Question

The first three terms of a G.P is are x+1, x-3 and x-1 find the value of x​

Answer 1

`\text{First term,}~ a = x+1\\\\\text{Common ratio,}~ r = (x-3)/(x+1)= (x-1)/(x-3)\\\\\text{Now,}\\\\~~~~~~(x-3)/(x+1) = (x-1)/(x-3)\\\\\\\implies (x-3)(x-3) = (x-1)(x+1)\\\\\\\implies (x-3)^2 = x^2 -1\\\\\\\implies x^2 -2\cdot 3x +3^2 =x^2 -1\\\\\\\implies -6x+9=-1\\\\\\\implies -6x = -1 -9\\\\\\\implies -6x = -10\\\\\\\implies x =(-10)/(-6)\\ \\\\\implies x = \frac 53`