Word Question for geometric series

Question

A square has sides 2 cm long. The midpoints
of each side are joined to form a second
square. The same procedure is done to the
this square to get a third square. If this
continues until 8 squares are formed, what
will be the total of all the perimeters?

Answer 1

Draw and label a diagram!

a₁ = 8

a₂ = 4√2

a₃ = 4

The common ratio is √2 / 2

 

S₈ = 8(1 - (√2/2)⁸ / (1 - √2/2)

 

Can you calculate and answer?