(i)[3]
A geometric progression starts with first term $a$ $(a \neq 0)$ and common ratio $r$, and its sum to infinity is $S$. A second geometric progression starts with the same first term $a$ but has common ratio $2r$ and sum to infinity $3S$. Determine the value of $r$.
(ii)[4]
In an arithmetic progression, the first term is $7$. The $n$th term equals $84$ and the $(3n)$th term equals $245$. Determine $n$.