TW-TST 1997 Problem 3

Let $n>2$ be an integer. Suppose that $a_{1},a_{2},...,a_{n}$ are real numbers such that $k_{i}=\frac{a_{i-1}+a_{i+1}}{a_{i}}$ is a positive integer for all $i$ (Here $a_{0}=a_{n},a_{n+1}=a_{1}$ ). Prove that $2n\leq a_{1}+a_{2}+...+a_{n}\leq 3n$ .