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Answer :
To find the common ratio of a sequence, you need to determine if the sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio.
Let's find the common ratio for the sequence: [tex]-71, -85.2, -102.24, -122.688[/tex].
Calculate the common ratio between the first and second terms:
[tex]r = \frac{-85.2}{-71} = 1.2[/tex]
Calculate the common ratio between the second and third terms to verify consistency:
[tex]r = \frac{-102.24}{-85.2} = 1.2[/tex]
Calculate the common ratio between the third and fourth terms to ensure it remains consistent:
[tex]r = \frac{-122.688}{-102.24} = 1.2[/tex]
Since the common ratio is consistently [tex]1.2[/tex] for each pair of terms, we can confirm that the sequence is geometric and the common ratio is [tex]1.2[/tex].
Therefore, the correct option is C. 1.2.
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