AHSME 1970 Problem 19

The sum of an infinite geometric series with common ratio $r$ such that $|r|<1$ is $15$, and the sum of the squares of the terms of this series is $45$. The first term of the series is $\textbf{(A) } 12 \textbf{(B) } 10 \textbf{(C) } 5 \textbf{(D) } 3 \textbf{(E) 2}$