A square is drawn by joining the mid-points of the sides of a square. A third square is drawn inside the second square in the same way and the processes continued indefinitely. If the side of the square is `10 c m` , find the sum of the areas of all the squares so formed.

Explanation

Side of the square is `10cm`
So, area of square `=100cm^2`
Now ,

Area of second Square is =`1/2​×`area of first square
`=50cm^2`

Area of third square `=25cm^2`

Thus, `100,50,25...` a G.P

With first term (a)=`100`

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