A sequence of ornamental patterns $P_1,P_2,P_3,\dots$ is created using colored beads. Pattern $P_1$ consists of a single bead. For $n\ge 2$, pattern $P_n$ is formed by adding a new outer layer of beads to $P_{n-1}$. The new outer layer for $P_n$ contains $4n-2$ beads. How many beads are there in pattern $P_{10}$?