math gre question
posted by luckybee .
in an infinite series of circles the radius of the second circle is one half the radius of the first circle and the radius of the third circle is one half the radius of the second circle. if the first circle has a radius of one inch which of the following statements best describe the sum of the areas of all the circles?
1. the sum of the area of all the circle converge to pi in^2
2. the sum of the areas of all the circles diverge from 2pi in^2
3. the sum of the areas of all the circles converge to 2pi in^2
4. the sum of the areas of all the circles diverge from pi in^2
my solution: i think it is number 4 because the radius ends up being zero.

a total of 920 adult and student ticket were sold for the school play. the number of student tickets sold was 16 less than twice the number of adult tickets.how many adult tickets were sold?

sum is pi(1^2 + (1/2)^2 + (1/4)^2 + ...)
= pi (1 + 1/4 + 1/16 + ...)
= pi (1/(1  1/4)) = pi (1/(3/4)) = 4pi/3
I think the answer they wanted was 2pi (#3) but 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...
and we have 1 + 1/4 + 1/16 + 1/64 + ...
a + s = 920
s = 2a16
a + 2a16 = 920
3a = 936
a = 312
s = 308 = 2*312  16
Respond to this Question
Similar Questions

Math
Circle C has radius 4 inches. Circle D had radius 9 inches. These two circles are connected. Point A,B,and E are points of tangency. Find AB. From point C to point D(which is the radius of circle C plus the raduis of circle D) it is … 
Geometry
A dartboard consists of five concentric circles. The radius of the smallest circle is about 1 inch. The radius of the second circle is about 3 inches longer. The radius of the third circle is about 1 inch longer than the previous circle. … 
Geomatric series
A 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 … 
maths
there are two circles touching each other at one point. The radius of bigger circle is 4cm and smaller is 1cm. A small third circle is drawn which touches both the first two circles at one point each. A common tangent passes through … 
GEOMETRY CIRCLES PLEASE
1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such … 
GEOMETRY CIRCLE
1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such … 
GEOMETRY CIRCLES PLEASE
HELP ME PLEASE. 1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is … 
PreCalc (Circles). Please help :(
Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn as shown dividing the circle of radius 5 into five regions: a circle of radius 1 and 4 annuuli (rings). What is the probability that a point chosen randomly from within … 
Math
A court is 94ft long by 50ft wide.It contains 3 circles, each with a diameter of 12 ft. Two of the circles are located at the free throw line with "half of each circle shaded" and the third circle is at the center. Within the third … 
Geometry
Write the General form equations for the following circles: 1. A circle with center (1, 6) and radius 4 2. A circle with center (6, 8) and radius 10 3. A circle with center (0, 3) and radius 2√3 4. A circle with center (0.5, 5.5 …