  We prove that certain sequences of finite continued fractions associated with
a 2-periodic continued fraction with period a,b>0 are moment sequences of
discrete signed measures supported in the interval [-1,1], and we give
necessary and sufficient conditions in order that these measures are positive.
For a=b=1 this proves that the sequence of ratios F_{n+1}/F_{n+2}, n\ge 0 of
consecutive Fibonacci numbers is a moment sequence.
