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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.16,8,4,...

Sagot :

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

[tex]16,8,4[/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, 16, 8, 4, ...

Since, common difference = 8 - 16 ≠ 4 - 8 , this is not arithmetic sequence.

Common ratio = T2/T1 = T3/T2 = 8/16 = 4/8 = 1/2 Because common ratio is are equal. Thus, given sequence is geometric sequence.

Hence the sequence is a geometric sequence and the common ratio = 1/2

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