1962 AHSME Problem 32

If x_{k+1} = x_k + \frac12 for k=1, 2, \ldots , n-1 and x_1=1, find x_1 + x_2 + \ldots + x_n.

\textbf{(A)}\ \frac{n+1}{2} \qquad \textbf{(B)}\ \frac{n+3}{2} \qquad \textbf{(C)}\ \frac{n^2-1}{2} \qquad \textbf{(D)}\ \frac{n^2+n}{4}\qquad \textbf{(E)}\ \frac{n^2+3n}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.