The geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...
There are three parameters which differentiate between which geometric sequence we're talking about.
The first parameter is the initial value of the sequence.
The second parameter is the quantity by which we multiply previous term to get the next term.
The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is 'a'
and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)
Then the sequence would look like
[tex]a, \: ar, \: ar^2, \: ar^3, \: \cdots[/tex]
(till the terms to which it is defined)
If the initial term is 'a', then the geometric sequence with common ratio = 2 would look like:
[tex]a, \: a(2), \: a(2)^2, \: a(2)^3, \: \cdots\\\\a, \: a(2), \: a(4), \: a(8), \: \cdots[/tex]
Checking all the options to see which one has got common ratio 2:
Initial term a = 14,
The geometric sequence with a = 14, and r = 2 would be:
[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]
The sequence 14, 16, 18, 20, ... doesn't match with it, so its not correct option.
Initial term a = 64,
The geometric sequence with a = 14, and r = 2 would be:
[tex]64, 64(2), 64(4), 64(8), \cdots\\\\64, 128, 256, 512, \cdots\\[/tex]
The sequence 64, 32, 16, 8, ... doesn't match with it, so its not correct option.
Initial term a = 64,
The geometric sequence with a = 14, and r = 2 would be:
[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]
The sequence 14, 28, 56, 112, ... matches with it, so its correct option.
Initial term a = 87,
The geometric sequence with a = 87, and r = 2 would be:
[tex]87, 87(2), 87(4), 87(8), \cdots\\\\87, 174, 348, 696, \cdots\\[/tex]
The sequence 87, 85, 83, 81, ... doesn't match with it, so its not correct option.
Thus, the geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...
Learn more about geometric sequence here:
https://brainly.com/question/2735005
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