The common ratio of the given geometric sequence is [tex]\frac{1}{2}[/tex].
What is geometric sequence and common ratio?
A geometric sequence is a sequence of numbers where each term after the first term is found by multiplying the previous one by a fixed non-zero number, called the common ratio.
Formula for finding the common ratio
[tex]r = \frac{a_{n} }{{a_{n-1} } }[/tex]
Where,
r is the common ratio
[tex]a_{n}[/tex] and [tex]a_{n-1}[/tex] are the nth and (n-1)th term of the geometric sequence.
According to the given question.
We have a geometric sequence 256, 128, 64, 32..
The first term of the given geometric sequence, [tex]a_{1} = 256[/tex]
The second term of the geometric sequence, [tex]a_{2}= 128[/tex]
Therefore,
The common ratio of the given geometric sequence = [tex]\frac{128}{256} =\frac{1}{2}[/tex]
Hence, the common ratio of the given geometric sequence is [tex]\frac{1}{2}[/tex].
Find out more information about common ratio geometric sequence here:
https://brainly.com/question/7642398
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