Home
Class 12
MATHS
If A(1),A(2),A(3),…,A(n) are n points in...

If `A_(1),A_(2),A_(3),…,A_(n)` are n points in a plane whose coordinates are `(x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n))` respectively. `A_(1)A_(2)` is bisected in the point `G_(1) : G_(1)A_(3)` is divided at `G_(2)` in the ratio `1 : 2, G_(2)A_(4)` at `G_(3)` in the1 : 3 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are `(x_(1)+x_(2)+.....+ x_(n))/(n)` and `(y_(1)+y_(2)+.....+ y_(n))/(n)`

Promotional Banner

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

The y-axis divides the line segment joining A(a_(1), b_(1)) and B(a_(2), b_(2)) in the ratio . . . . .

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= a_(2)= 1, a_(n)= a_(n-1) + a_(n-2), n gt 2

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

Differentiate a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)

Write the first five terms of the sequences in obtain the corresponding series: a_(1)= 2, a_(n)= a_(n-1) + 3, AA n ge 2

The points A(x_(1), y_(1)) , B(x_(2), y_(2)) and C(x_(3), y_(3)) are the vertices of Delta ABC and AD is a median in Delta ABC . Find the coordinates of a point G on median AD such that AG : GD = 2 : 1

If a_(1),a_(2),a_(3),"….",a_(n) are in AP, where a_(i)gt0 for all I, the value of (1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n)) is

Write the first five terms of each of the sequences and obtain the corresponding series: a_(1) =a_(2) =2 , a_(n) =a_(n-1) -1, n gt 2

What does a_(1) + a_(2) + a_(3) + …..+ a_(n) represent