tangent at a point C1 on the curve y=x^3 meets the curve again at C2 .the tangent at C2 meets the curve at C3, and soo on, so that the abscissa of c1,c2,c3.....,Cn form a G.P. find the ratio of area of triangle C1C2C3 to the area of triangle C2C3C4

Dear Student,
Suppose the absiccas of the points are a,ar,ar^2,ar^3……..
          So, the co ordinates of the four points will be
          C1(a,a^3), C2(ar,a^3r^3), C3(ar^2,a^3r^6),C4(ar^3,a^3r^9)
          As, they are all situated on the curve
         So, putting the formula of area of triangle by the ponts we get,
         Triangle C1C2C3: triangle C2C3C4
        = a^4[ r^3-r^6+r^7-r+ r^2-r^5]/ a^4[ r^7 -r^10+r^11-r^5+r^6-r^9]
         = 1/r^4
        ( wgrre r= c2/c1).