1979 AHSME Problem 14

In a certain sequence of numbers, the first number is 1, and, for all n\ge 2, the product of the first n numbers in the sequence is n^2. The sum of the third and the fifth numbers in the sequence is

\textbf{(A) }\frac{25}{9}\qquad \textbf{(B) }\frac{31}{15}\qquad \textbf{(C) }\frac{61}{16}\qquad \textbf{(D) }\frac{576}{225}\qquad \textbf{(E) }34

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