The sum of three terms of a geometric progression is 105. If we subtract 15 from the third term, we will have an arithmetic progression. Determine the two progressions.
In the context of our task,

(1) plus (2) gives,

from which

by putting (1) into it, we get:

from which

and thus

Therefore, the sought terms are:

$$
\begin{gathered}
a + a q + a q^{2} = 105 \\
2 a q = a + \left(a q^{2} - 15\right) \\
3 a q = 90 \text { or } a q = 30 \\
a = \frac{30}{q}
\end{gathered}
$$

$$
2 q^{2} - 5 q + 2 = 0
$$

$$
q = 2 \text { and } q' = \frac{1}{2}
$$

$$
a = 3 \text { and } a' = 60
$$

$15, 30, 60 ; \quad 15, 30, 45 ; \quad 60, 30, 15 ; \quad 60, 30, 0$.