\[1,\ 3,\ 5,\ 7,\ 9 \Longrightarrow d = 2\]
\[a_{n} = a_{1} + (n - 1)d =\]
\[= 1 + (n - 1) \cdot 2 = 1 + 2n - 2 =\]
\[= 2n - 1 \Longrightarrow a_{n} = 2n - 1.\]