Answer:
The sequence is geometric
The common ratio is 0.5
Step-by-step explanation:
In the arithmetic sequence, there is a common difference between each two consecutive terms
In the geometric sequence, there is a common ratio between each two consecutive terms
Let us check the given sequence
∵ The first 3 terms are 12, 6, 3
∵ 6 - 12 = -6
∵ 3 - 6 = -3
∵ There is no common difference between the consecutive terms
∴ The sequence is not an arithmetic sequence
∵ 6 ÷ 12 = 0.5
∵ 3 ÷ 6 = 0.5
∴ There is a common ratio between each two consecutive terms
∴ The sequence is a geometric sequence
∴ The common ratio is 0.5
Given sequence is geometric sequence and common ratio between consecutive term is [tex]\frac{1}{2}[/tex] .
In Arithmetic sequence , common difference between consecutive terms should be equal.
In Geometric sequence, common ratio between consecutive terms should be equal.
Given sequence, 12, 6, 3, ...
Since, common difference = [tex]6-12\neq 3-6[/tex] , this is not arithmetic sequence.
Common ratio = [tex]\frac{6}{12}=\frac{3}{6}=\frac{1}{2}[/tex] Because common ratio is are equal. Thus, given sequence is geometric sequence.
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