Given a geometric progression -9.3, -1, .. find the product of its first five terms

Let’s find what the denominator q of this geometric progression is equal to.

By the statement of the problem, the first member b1 of this geometric sequence is -9, the second member b2 of this geometric sequence is 3, and the third member b3 of this geometric sequence is -1.

Using the definition of a geometric progression, we find the denominator q of this progression:

q = b2 / b1 = 3 / (-9) = -1/3.

Knowing b3 and q, we find b4:

b4 = b3 * q = -1 * (-1/3) = 1/3.

Knowing b4 and q, we find b5:

b5 = b4 * q = (1/3) * (-1/3) = -1/9.

We find the product of the first five members of this progression:

(-9) * 3 * (-1) * (1/3) * (-1/9) = (-9) * (-1/9) * 3 * (1/3) * (-1) = -one.

Answer: the product of the first five members of this progression is -1.