Continued Fractions I

An article introducing continued fractions with some simple puzzles for the reader.

Fibonacci Factors

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

Golden Fibs

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

Golden Powers

Stage: 5 Challenge Level:

The famous golden ratio is $g={\sqrt5 + 1 \over 2}$. Prove that $g^2=g+1$.

Let $g^n = a_ng + b_n$. Find the sequences of coefficients $a_n$ and $b_n$.