A number of interlocking rings each 1 cm thick are hanging from a peg. The top ring has an outside diameter of 20 cm. The outside diameter of each of the outer rings is 1 cm less than that of the ring above it. The bottom ring has an outside diameter of 3 cm. What is the distance from the top of the top ring and the bottom of the bottom ring?

Here is a picture of what this thing looks like:

So, this is my attempt:

t1 = 20 cm d = -1 cm tn = 3 cm n = ?Sn = ? (We are trying to figure out Sn?)

First, I try to solve for n:

tn = t1 + (n-1)d

3 = 20 + (n-1)-1

3 = 20 + (n+1)

-17 = n + 1

n = -18

Now, I try to solve for Sn and plugging in the tn I found:

Sn = n/2 (t1 + tn)

Sn = -18/2 (20 + 3)

Sn = -207

The number shouldn't be positive...

The answer is actually 173 cm... I'm not sure where I went wrong... :/