In the figure above, midpoints of the sides of a square are joined to form another smaller square, and the same process is repeated 1000 times. If the area of the smallest square is 100km², what is the area of the largest square?
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Side of the square is 10cm
So, area of square =100cm
2
Now Area of second Square is = 21
× area of first square=50cm 2
Area of third square =25cm 2
Clearly 100,50,25... a G.P
With first term (a)=100
and common ration (r)= 21
So, Sum of all square = Sum of G.P to infinity = 1−ra= 1− 21100=200cm 2
Step-by-step explanation:
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