Thursday

April 24, 2014

April 24, 2014

Posted by **nick** on Thursday, April 19, 2012 at 8:41pm.

(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.

- math -
**Reiny**, Thursday, April 19, 2012 at 10:26pmI 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

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