Proving that $n$-cycle has order $n$

Question

I'm trying trying to prove that an $n$-cycle in some symmetric group has order $n$, but I don't know where to start. Would appreciate some hints.

Answer 1

For each $n$-cycle $w$, it has a representation $(a_1a_2...a_n)$. $w^{n-1}(a_1)=a_{n}\neq a_1$ so $w$ has order at least $n$.