Problem - 3171
Suppose no term in an arithmetic sequence $\{a_n\}$ equals $0$. Let $S_n$ be the sum of its first $n$ terms. If $S_{2n-1} = a_n^2$, find the expression for its $n^{th}$ term $a_n$.
$$S_{2n-1}=a_n\cdot n \implies a_n^2=a_n(2n-1)\implies a_n=\boxed{2n-1}\quad(\because a_n\ne 0)$$