The correct option is (C) 8 to 1.
The ratio of the 8th term in the sequence to the 5th term is 8:1.
The geometric sequence is a number sequence in which each term following the first is found through multiplying the preceding one by a fixed non-zero value known as the common ratio r.
Now, according to the question;
The geometric sequence can be written as;
[tex]a_{n}=2 a_{n-1}[/tex]
Where, r = 2.
In G.P;
[tex]a_{n}=a_{1} r^{n-1}[/tex]
Where [tex]a_{n}[/tex] shows nth term of an G.P.
and [tex]\mathrm{a}_{1}[/tex] show the first term of the G.P.
To evaluate the ratio of the 8th term to the 5th term;
[tex]\begin{aligned}&a_{8}=a_{1} 2^{8-1} \\&a_{8}=2^{7} a_{1} \\&a_{5}=a_{1} 2^{5-1} \\&a_{5}=2^{4} a_{1}\end{aligned}[/tex]
So, ratio of a₈ to a₅ is;
= [tex]2^{7} a_{1}: 2^{4} a_{1}[/tex]
= [tex]\frac{128}{16}: 1[/tex]
= 8 : 1
Therefore, a 8th term in this series has an 8:1 ratio to the 5th term.
To know more about the geometric sequence, here
https://brainly.com/question/1509142
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