I have to solve the following problem:
Let $q \in \mathbb{R}$. If $a_{n+1}=qa_n$ for all $n \in \mathbb{N}$ then $a_n=a_0q^n$ for all $n \in \mathbb{N}$.
My first idea was to use induction but I dont know exactly how to start. Perhaps someone can give me a hint?
Thanks a lot in advance.