Find the common ratio of the geometric sequence. $\frac{1}{8 \pi}, \frac{1}{(8 \pi)^{2}}, \frac{1}{(8 \pi)^{3}}, \frac{1}{(8 \pi)^{4}},....$
A) $\frac{1}{\pi^{2}}$
B) $\frac{1}{\pi}$
C) $\frac{1}{8 \pi}$
D) $\frac{1}{8}$
E) $\frac { 1 } { ( 8 \pi ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

In a geometric sequence, each term is obtained by multiplying the previous term by a constant called the common ratio. We can find the common ratio of this sequence by dividing any term by its previous term. For example:
$$\frac{\frac{1}{(8\pi)^2}}{\frac{1}{8\pi}} = \frac{8\pi}{(8\pi)^2} = \frac{1}{8\pi}$$
So the common ratio is $\frac{1}{8\pi}$, which is choice (C).

Find the Common Ratio of the Geometric Sequence 18π,1(8π)2,1(8π)3,1(8π)4,....\frac{1}{8 \pi}, \frac{1}{(8 \pi)^{2}}, \frac{1}{(8 \pi)^{3}}, \frac{1}{(8 \pi)^{4}},....8π1​,(8π)21​,(8π)31​,(8π)41​,....

Find the Common Ratio of the Geometric Sequence $\frac{1}{8 \pi}, \frac{1}{(8 \pi)^{2}}, \frac{1}{(8 \pi)^{3}}, \frac{1}{(8 \pi)^{4}},....$