You are given a geometric progression (b n), for which b5 = -8, b6 = -32. Find the denominator of the progression.

You are given a geometric progression {bn} for which the equalities b5 = -8 and b6 = -32 are true. At the request of the task, we calculate the denominator q of the given geometric progression.
As you know, in order to have a complete picture of the geometric progression {bn}, it is enough to know only two of its parameters: the first term b1 and the denominator q. In the task, the fifth b5 and sixth b6 members of a geometric progression are given. Let’s use the definition of a geometric progression. We have: q = b6: b5 = (-32): (-8) = 4.
Answer: If b5 = -8 and b6 = -32, then the denominator of the progression is 4.