Question

If $x_1=a,y_1=b$ and $x_i^{\prime }s$ from an G.P. common ratio $2$ and $y_i^{\prime }s$ form a G.P. with common ratio $3$, then find the co-ordinates of $G$,centroid.

Answer 1

Given, $x_1=a,y_2=b,r_1=2,r_2=3$

$\implies

\dfrac{\Sigma x_i}{n} = \dfrac{1}{n} \left[\dfrac{1.(2^n - 1)}{2 - 1}\right] = \dfrac{1}{n}(2^n - 1)\dfrac{\Sigma y_i}{n} = \dfrac{1}{n} \left[\dfrac{2.(3^n - 1)}{3 - 1}\right] = \dfrac{1}{n}(3^n - 1)\therefore$is$\left[\dfrac{1}{n}(2^n - 1), \dfrac{1}{n}(3^n - 1)\right]$