Question

If $x_1=a,y_1=b$ and $x_i^{\prime }s$ from an A.P. common difference $2$ and $y_1^{\prime }s$ form an A.P. with common difference $4$, then find the co-ordinates of $G$, the centroid.

Answer 1

Given, $x_1=a,y_1=b$

$\Sigma x_i=x_1+x_2+x_3+$____ $+x_n$

$=\frac{n}{2}[2a+(n-1\left)2\right]$
$\therefore \frac{\Sigma x_i}{n}=a+(n-1)$. Similarly, $\frac{\Sigma y_i}{n}=b+(n-1)2$
$\therefore G$ is $[a+(n-1),b+(n-1\left)2\right]$