The $1^{\text{st}}$, $2^{\text{nd}}$ and $3^{\text{rd}}$ terms of a geometric progression are also the $1^{\text{st}}$, $4^{\text{th}}$ and $6^{\text{th}}$ terms, respectively, of an arithmetic progression.

The sum to infinity of the geometric progression is $12$.

Find the $1^{\text{st}}$ term of the geometric progression.