## 2bornot2b Group Title What is the difference between a Fibonacci sequence and a Lucas sequence? 2 years ago 2 years ago

1. across

The Fibonacci numbers are a particular example of a Lucas sequence.

2. 2bornot2b

Can you be a bit more specific, something like typing down the numbers will be better for me to understand. ..

3. across

A Lucas sequence is defined as follows:$x_n=Px_{n-1}+Qx_{x-2}\text{, where }P,Q\in\mathbb{Z}.$ The Fibonacci sequence has it that $$P=Q=1$$ and is as follows:$1,1,2,3,5,8,13,\dots$However, What if I were to change $$P=Q=2$$? Then I would get:$1,1,4,10,28,76,\dots$which is not the Fibonacci sequence but it is a Lucas sequence.