1982 AMC 12 Question 8

By definition $r!=r(r-1)\cdots1$ and $\binom jk=\frac{j!}{k!(j-k)!},$ where $r,$ $j,$ $k$ are positive integers and $k\lt j.$ If $\binom n1,$ $\binom n2,$ $\binom n3$ form an arithmetic progression with $n\gt3,$ then $n$ equals