# You are given a geometric progression (bn) in which b5 = 15, b8 = -1875. Find the denominator of the progression.

March 25, 2021 | education

| By condition:

b5 = 15;

b8 = – 1875.

We represent b5 as the product of the first term of the progression b1 and the denominator of the progression q:

b5 = b1 * q ^ 4.

We represent b8 as the product of the first term of the progression b1 and the denominator of the progression q:

b8 = b1 * q ^ 7.

Thus, one can come to a system of equations:

b1 * q ^ 4 = 15;

b1 * q ^ 7 = – 1875.

In the first equation of the system, we express b1 through q:

b1 = 15 / q ^ 4.

We substitute the resulting expression into the second equation of the system:

(15 / q ^ 4) * q ^ 7 = – 1875;

15q ^ 7 / q ^ 4 = – 1875;

15q ^ (7 – 4) = – 1875;

15q ^ 3 = – 1875;

q ^ 3 = – 1875/15;

q ^ 3 = – 125;

q = ³√ (- 125);

q = – 5.

Answer: q = – 5.

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