2. The fourth term of a geometric progression $b_{4}=\frac{1}{25}$, the fifth term $b_{5}=\frac{1}{125}$. Find the sum of the first five terms.
Solution: $b_{4}=\frac{1}{25} ; \quad b_{5}=\frac{1}{125}, S_{5}=$ ?

$$
\left\{\begin{array}{l}
b_{1} \cdot q^{3}=\frac{1}{25}, \quad q=\frac{1}{125} \cdot \frac{25}{1}=\frac{1}{5}, \quad S_{5}=\frac{5\left(1-\left(\frac{1}{5}\right)^{5}\right)}{1-\frac{1}{5}}=\frac{781}{125} \\
b_{1} \cdot q^{4}=\frac{1}{125} ; \quad b_{1}=5
\end{array}\right.
$$