30. a) Find the sum of the first 15 terms of an arithmetic progression where the first term is 0, and the common difference is $\frac{1}{3}$.

b) Find the product of the first 15 terms of a geometric progression where the first term is 1, and the common ratio is $\sqrt[3]{10}$.
30. a) According to the formula obtained in problem $29 a)$

$$
S_{n}=u_{1} n+\frac{n(n-1)}{2} d=\frac{15 \cdot 14}{2} \cdot \frac{1}{3}=35
$$

b) According to the formula obtained in problem 29 b),

$$
\begin{aligned}
& P_{n}=u_{1}^{n} q^{\frac{n(n-1)}{2}}=(\sqrt[3]{10})^{\frac{15 \cdot 14}{2}}= \\
& =10^{\frac{15 \cdot 14}{2} \cdot \frac{1}{3}}=10^{35} .
\end{aligned}
$$