Let $S$ be the sum of an infinite geometric series with first term $a_1$ and common ratio $r$. Suppose $S = \sum_{n=1}^{\infty} a_1 r^{n-1}$ and let $T = \sum_{n=1}^{\infty} (a_n)^2$, where $a_n$ is the $n$-th term of the series. If $S = 6$ and $T = 18$, which of the following statements about the series are true?