## Two lemmas on linear sequences of order two

Note: My English is so bad but don’t worry about that! 🙂

A sequence $(a_n)$ is called linear of order two if there are real numbers $p,q$ such that $a_{n+2}=pa_{n+1}+qa_n\;\forall n=1,2,3,...$

In this topic we’ll use ideas in proofs of two following lemmas to solve some Olympiad problems.