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

(a) Determine the number of terms, n, if 3+3^2+3^3+..........+3^n= 9840.

(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 5:49pm
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 is the sum of the areas of the circles? Express your answer as an exact fraction.

- Pre Calculus -
**Steve**, Sunday, November 25, 2012 at 8:42pm
9840 = 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 8:47pm
if 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

## Answer This Question

## Related Questions

- Series and sequences - Three numbers a,b, and c form a geometric series so that ...
- Math *URGENT - Please give the answers and solutions for each. 1.If the second ...
- Pre-Calculus - Q.Determine the sum of each infinite geometric series. t_1= 8 r...
- algebra - Can someone please help me with this problem? Thanks! Evaluate the ...
- SeQuEnCeS and SeRiEs: HELP PLZ! - The first three terms of the sequence -8,x,y,...
- maths - three number form an arithmetric sequence. Their sum is 24. A)If 'a' is ...
- calculus - which number should be subtracted from each of the three numbers 5, ...
- Math - The first two terms in a geometric series is 12. The sum of the first ...
- Pre Calculus - The third term of a geometric series is 24 and the fourth term is...
- arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

More Related Questions