Irene gave points to students who performed well in class. The $1$\textsuperscript{st} student got $2$ points, the $2$\textsuperscript{nd} student got $6$ points, the $3$\textsuperscript{rd} student got $10$ points, the $4$\textsuperscript{th} student got $14$ points, and so on. Given that the points won by the students formed an arithmetic sequence, find the number of points won by the $11$\textsuperscript{th} student. 
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