Question

A number of circles touch each ather. The area of the smallest circle is 4picm2 and each consecutive circle has area 9/4 times that of the previous one. If the distance AB=665/8. Line AB passes at the centre of the circles. How many circles are there?

Answer 1

The smallest circle has a radius of 2.
Each circle's radius is 3/2 that of the previous one.

If there are n circles, then since the first and last circles are only traversed halfway, we have

2 + 4(3/2) + 4(3/2)^2 + ... + 2(3/2)^(n-1) = 665/8

Hmmm. I get a non-integer solution for n.

Below are the lengths of AB as the number of circles increases
2
4*3/2 = 6; 2+6 = 8
6*3/2 = 9; 8+9 = 17
9 * 3/2 = 27/2; 17 + 27/2 = 61/2
and so on.

Have I misread something?

Answer 2

it saids 423+5123