Geometric series have the same ratio. The series which is a geometric series is 1, 3, 9, 27.
<h3>What is a geometric series?</h3>
A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A.) 0.1 0.3 0.5 0.7
To check if the series is geometric series, find the quotient.
![r_1=\dfrac{0.3}{0.1} = 3\\\\r_2 = \dfrac{0.5}{0.3} = 1.66](https://tex.z-dn.net/?f=r_1%3D%5Cdfrac%7B0.3%7D%7B0.1%7D%20%3D%203%5C%5C%5C%5Cr_2%20%3D%20%5Cdfrac%7B0.5%7D%7B0.3%7D%20%3D%201.66)
Since the ratio is different this is not a geometric series.
B.) 1 3 9 27
To check if the series is geometric series, find the quotient.
![r_1=\dfrac{3}{1} = 3\\\\r_2 = \dfrac{9}{3} = 3](https://tex.z-dn.net/?f=r_1%3D%5Cdfrac%7B3%7D%7B1%7D%20%3D%203%5C%5C%5C%5Cr_2%20%3D%20%5Cdfrac%7B9%7D%7B3%7D%20%3D%203)
Since the ratio is the same this is a geometric series.
C.) 19 17 15 13
To check if the series is geometric series, find the quotient.
![r_1=\dfrac{17}{19} = 0.8947\\\\r_2 = \dfrac{15}{17} = 0.8823](https://tex.z-dn.net/?f=r_1%3D%5Cdfrac%7B17%7D%7B19%7D%20%3D%200.8947%5C%5C%5C%5Cr_2%20%3D%20%5Cdfrac%7B15%7D%7B17%7D%20%3D%200.8823)
Since the ratio is different this is not a geometric series.
D.) 0.4 0.9 1.5 2.2
To check if the series is geometric series, find the quotient.
![r_1=\dfrac{0.4}{0.9} = 0.4444\\\\r_2 = \dfrac{0.9}{1.5} = 0.6](https://tex.z-dn.net/?f=r_1%3D%5Cdfrac%7B0.4%7D%7B0.9%7D%20%3D%200.4444%5C%5C%5C%5Cr_2%20%3D%20%5Cdfrac%7B0.9%7D%7B1.5%7D%20%3D%200.6)
Since the ratio is different this is not a geometric series.
Learn more about Geometric Series:
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