In a square, one can connect the midpoints of adjacent sides to form second square. One can then connect the midpoints of adjacent sides of the second square to form a third square and continue in the same manner to form more squares successively.
Suppose the area of the initial square is 1 square unit, and consider the sequence of areas of the squares formed in this way.
Do these area form a geometric sequence? If they do, what are the first term and common ratio of the geometric sequence? If they do not, what sort of sequence do they form?