Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form 12,6,3

Given sequence is geometric sequence and common ratio between consecutive term is   .

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 =   , this is not arithmetic sequence.

Common ratio =      Because common ratio is are equal. Thus, given sequence is geometric sequence.

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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

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step-by-step explanation: