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 areas form a geometric sequence? . Yes!
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?