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November 24, 2014

November 24, 2014

Posted by **HanuMath25/11** on Sunday, November 25, 2012 at 5:23pm.

(b) Three numbers, a, b and c form a geometric series so that a+b+c = 35 and abc = 1000. What are the values of a, b and c ?

- Pre Calculus -
**HanuMath25/11**, Sunday, November 25, 2012 at 5:49pmA fractal is created: A circle is drawn with radius 8 cm. Another circle is drawn with half the radius of the previous circle. The new circle is tangent to the previous circle. Suppose this pattern continues through five steps. What is the sum of the areas of the circles? Express your answer as an exact fraction.

- Pre Calculus -
**Steve**, Sunday, November 25, 2012 at 8:42pm9840 = 3(1-3^n)/(1-3)

n = 8

a+ar+ar^2 = 35

a*ar*ar^2 = 1000

a(1+r+r^2) = 35

a^3 r^3 = 1000

by inspection, since 1000 = 2^3 * 5^3, a and r are 2 and 5.

the only factors of 35 are 5 and 7, so

a=5

r=2

(a,b,c) = (5,10,20)

- Pre Calculus -
**Steve**, Sunday, November 25, 2012 at 8:47pmif only one circle of each radius is drawn, the radii are

8,4,2,1,1/2,1/4

pi(8^2 + 4^2 + 2^2 + 1^2 + (1/2)^2 + (1/4)^2) = 1365/16 pi

Note that since

sum(1,infinity) 1/n^2 = pi^2/6, if the sequence were carried out forever, the area would be

pi * 64 * pi^2/6

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