Would someone help me with this problem?

Define the sequence $\displaystyle \{a_n\}$ in a metric space $\displaystyle (X,d)$ such that $\displaystyle d(a_{n+2},a_{n+1})\leq cd(a_{n+1},a_n)$ for $\displaystyle c\in (0,1)$. Show that $\displaystyle \{a_n\}$ is Cauchy.