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

Question

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

Valentine Bouyer · Accepted Answer

Final Answer : C, Explanation :   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: 1 ( 8 π ) 2 1 8 π = 8 π ( 8 π ) 2 = 1 8 π \frac{\frac{1}{(8\pi)^2}}{\frac{1}{8\pi}} = \frac{8\pi}{(8\pi)^2} = \frac{1}{8\pi} 8 π 1 ​ ( 8 π ) 2 1 ​ ​ = ( 8 π ) 2 8 π ​ = 8 π 1 ​ So the common ratio is $\frac{1}{8\pi}$, which is choice (C).

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

A) $1π2\frac{1}{\pi^{2}}$
B) $1π\frac{1}{\pi}$
C) $18π\frac{1}{8 \pi}$
D) $18\frac{1}{8}$
E) $2\frac { 1 } { ( 8 \pi ) ^ { 2 } }$

Definitions

Learning Objectives

Learning Objectives

Related questions