A rope is swinging in such a way that the length of the arc is decreasing geometrically. If the first arc is 18 feet long and the third arc is 8 feet long, what is the length of the second arc?

The correct answer to this question is this one:

geometric means you multiply by some factor to get the next number

you start at 18

the next number is 18*K (K is the factor)

the 3rd number is 18*k*k

but we know the third number is 8

So x = 12.