The second and fourth terms of a geometric progression are 6 and 1.5 respectively. Find the common ratio and the first term, S term, sum to infinity of the progression.

For the second term:

For the fourth term:

Divide equation (2) by equation (1):

Taking the square root, $r = \pm \sqrt{\frac{1}{4}} = \pm \frac{1}{2}$.
Since the given terms (6 and 1.5) are positive, we assume the common ratio is positive unless otherwise specified, leading to a progression with all positive terms.

Substitute $r = \frac{1}{2}$ into equation (1):

The common ratio is $\boxed{\frac{1}{2}}$ and the first term is $\boxed{12}$.

For the 8th term, $n=8$.

The 8th term is $\boxed{\frac{3}{32}}$.

Here, $a=12$ and $r=\frac{1}{2}$. Since $|r| = \left|\frac{1}{2}\right| = \frac{1}{2} < 1$, the sum to infinity exists.

The sum to infinity of the progression is $\boxed{24}$.