The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... where the next number in the sequence is simply the sum of the previous two numbers. As more terms are added to the sequence, the ratio of adjacent terms approaches the golden ratio.

What is the ratio of the tenth term to the ninth term shown, expressed as a decimal rounded to the nearest thousandth?

Question

The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... where the next number in the sequence is simply the sum of the previous two numbers. As more terms are added to the sequence, the ratio of adjacent terms approaches the golden ratio.
 
What is the ratio of the tenth term to the ninth term shown, expressed as a decimal rounded to the nearest thousandth?

kinggeorge · Answer

Well, the 10th term is 34, and the 9th term is 21, so just calculate $${34 \over 21}$$ with a calculator...

anonymous · Answer

1.619 correct?

anonymous · Answer

yes

anonymous · Answer

the farther out you go, the close  you will get to 
$$\frac{1+\sqrt{5}}{2}$$

kinggeorge · Answer

Otherwise known as the golden ratio or "phi"

anonymous · Answer

solution to 
$$x^2=x+1$$ or 
$$x=1+\frac{1}{x}$$ a number that is equal to one plus its reciprocal