The common ratio of the given sequence is equal to \(\frac{1}{4}\).
What is a common ratio?
" Common ratio is defined as the ratio of two consecutive terms that remain constant for a given sequence."
Formula used
Common ratio \(= \frac{a_{n} }{a_{n-1} }\)
\(a_{n} =\) \(nth\) term
\(a_{n-1} =\) \((n-1)th\) term
According to the question,
Given sequence,
\(\frac{2}{3}, \frac{1}{6} ,\frac{1}{24} , \frac{1}{96} ,.....\)
Common ratio
\(= \frac{a_{2} }{a_{1} }\)
\(= \frac{\frac{1}{6} }{\frac{2}{3} }\)
\(= \frac{1}{4}\)
Common ratio
\(= \frac{a_{3} }{a_{2} }\)
\(= \frac{\frac{1}{24} }{\frac{1}{6} }\\\\= \frac{1}{4}\)
Hence, Option (B) is the correct answer.
Learn more about common ratio here
brainly.com/question/13637951
#SPJ2
