If the coefficients of $2^{nd},3^{rd}\:and\:4^{th}$ terms in the expansion of $(1+x)^{2n} $ are in A.P., then $n=?$

Question

$\begin{array}{1 1} 1 \\ \frac{5}{2} \\ \frac{7}{2} \\ No\;such\;n\;exists \end{array} $