The common ratio of the given sequence is equal to [tex]\frac{1}{4}[/tex].
" Common ratio is defined as the ratio of two consecutive terms that remain constant for a given sequence."
Formula used
Common ratio [tex]= \frac{a_{n} }{a_{n-1} }[/tex]
[tex]a_{n} =[/tex] [tex]nth[/tex] term
[tex]a_{n-1} =[/tex] [tex](n-1)th[/tex] term
According to the question,
Given sequence,
[tex]\frac{2}{3}, \frac{1}{6} ,\frac{1}{24} , \frac{1}{96} ,.....[/tex]
Common ratio
[tex]= \frac{a_{2} }{a_{1} }[/tex]
[tex]= \frac{\frac{1}{6} }{\frac{2}{3} }[/tex]
[tex]= \frac{1}{4}[/tex]
Common ratio
[tex]= \frac{a_{3} }{a_{2} }[/tex]
[tex]= \frac{\frac{1}{24} }{\frac{1}{6} }\\\\= \frac{1}{4}[/tex]
Hence, Option (B) is the correct answer.
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