This image contains a set of problems on geometric progressions. Let's go through the first one:

1. In the geometric progression $(b_n)$, it is known that $b_1 = 2$ and $q = -2$. Find the fifth term of this progression.

The general formula for the $n$-th term of a geometric progression is:
$b_n = b_1 \cdot q^{n-1}$ Substituting the given values: $b_5 = 2 \cdot (-2)^{4} = 2 \cdot 16 = 32$ So, the fifth term is $b_5 = 32$.

Would you like a detailed explanation for this solution or help with another problem?

Here are some follow-up questions to expand on the topic:

1. How do you find the sum of the first $n$ terms of a geometric progression?
2. What happens if the common ratio $q$ is a fraction?
3. How can you determine if a sequence is geometric?
4. What are the applications of geometric progressions in real life?
5. How does changing the first term affect the progression?

Tip: When solving geometric progressions, always check the sign of the common ratio $q$ as it influences the pattern of the terms.