Question

Area A sequence of smaller squares is formed by connecting the midpoints of the sides of a larger square.
(a) If the area of the largest square is 1 square unit,
determine the first five terms of a sequence that
describes the area of each successive square.
(b) Use a formula to sum the areas of the first 10
squares.

Answer 1

I hope you made a sketch
side of square 1 = 1
area = 1

side of square 2 = √2/2
area = 1/2

side of square 3 = 1/2
area of square 3 = 1/4

side of square 4 = √2/4
area of square 4 = 2/16 = 1/8

areas are : 1 , 1/2, 1/4, 1/8 , 1/16 ...


looks like a GS , where a=1, r = 1/2

sum(10) = a(1 - r^10) / (1-r)
= 1(1 - (1/2)^10 )/(1/2)
= 2(1 - 1/1024)
= 2(1023/1024)
= 1023/512

Answer 2

please explain where th square root of 2 came from