Asked by Kayelyn Rooney on Jul 09, 2024

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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,....

A) 1π2\frac{1}{\pi^{2}}π21
B) 1π\frac{1}{\pi}π1
C) 18π\frac{1}{8 \pi}8π1
D) 18\frac{1}{8}81
E) 1(8π) 2\frac { 1 } { ( 8 \pi ) ^ { 2 } }(8π) 21

Common Ratio

In a geometric sequence, the constant factor by which each term is multiplied to get the next term.

Geometric Sequence

A series of numbers in which each subsequent number is obtained by multiplying the preceding number by a constant, non-zero value known as the common ratio.

  • Ascertain the standard ratio integral to geometric progressions.
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Valentine Bouyer

1 week ago

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(8π)218π=8π(8π)2=18π\frac{\frac{1}{(8\pi)^2}}{\frac{1}{8\pi}} = \frac{8\pi}{(8\pi)^2} = \frac{1}{8\pi}8π1(8π)21=(8π)28π=8π1
So the common ratio is $\frac{1}{8\pi}$, which is choice (C).