(a)[3]
For a geometric progression, the second term is $24\%$ of the sum to infinity. Determine the possible values of the common ratio.
(b)[6]
In the arithmetic progression $P$, the first term is $a$ and the common difference is $d$. In the arithmetic progression $Q$, the first term is $2(a + 1)$ and the common difference is $(d + 1)$. You are told that $\frac{\text{5th term of } P}{\text{12th term of } Q} = \frac{1}{3}$ and $\frac{\text{Sum of first 5 terms of } P}{\text{Sum of first 5 terms of } Q} = \frac{2}{3}$. Determine the values of $a$ and $d$.