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Answer :
Answer:
1, 2, 3, 5
Step-by-step explanation:
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The sequence that shows geometric progression are options A), B), C), and E) and this can be determined by finding the geometric ratio.
Check all the options in order to determine which sequence is the geometric sequence.
A) 10, 7.5, 5.625, 4.21875,...
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{7.5}{10}[/tex]
r = 0.75
Ratio between second and third term:
[tex]\rm r =\dfrac{5.625}{7.5}[/tex]
r = 0.75
So, yes this sequence is in geometric progression.
B) 160, 40, 10, 2.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{40}{160}[/tex]
r = 0.25
Ratio between second and third term:
[tex]\rm r =\dfrac{10}{40}[/tex]
r = 0.25
So, yes this sequence is in geometric progression.
C) 20, 70, 245, 857.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{70}{20}[/tex]
r = 3.5
Ratio between third and fourth term:
[tex]\rm r =\dfrac{857.5}{245}[/tex]
r = 3.5
So, yes this sequence is in geometric progression.
D) 13, 16.5, 20, 23.5, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{16.5}{13}[/tex]
r = 1.27
Ratio between third and fourth term:
[tex]\rm r =\dfrac{23.5}{20}[/tex]
r = 1.175
So, no this sequence is not in geometric progression.
E) 5, 5.5, 6.05, 6.655, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{5.5}{5}[/tex]
r = 1.1
Ratio between third and fourth term:
[tex]\rm r =\dfrac{6.655}{6.05}[/tex]
r = 1.1
So, yes this sequence is in geometric progression.
F) 16, 17.1, 18.2, 19.3, …
Check from the geometric ratio whether the above sequence is a geometric sequence or not.
Ratio between first and second term:
[tex]\rm r =\dfrac{17.1}{16}[/tex]
r = 1.07
Ratio between third and fourth term:
[tex]\rm r =\dfrac{19.3}{18.2}[/tex]
r = 1.06
So, no this sequence is not in geometric progression.
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https://brainly.com/question/4853032
