Next term of the given sequence \(3, 9, 27, 81, . . .\)is \(243\).
What is geometric sequence?
"Geometric sequence is defined as the sequence ratio between the consecutive terms is always constant."
Formula used
Geometric sequence
\(a_{1} , a_{2} ,a_{3} ,a_{4} ,a_{5} ,.......\)
common ratio 'r' = \(\frac{a_{2}}{a_{1} } =\frac{a_{3} }{a_{2}} =\frac{a_{4} }{a_{3}} =.......\)
According to the question,
Given sequence,
\(3, 9, 27, 81, . . .\)
Substitute the value in the formula of common ratio we get,
common ratio 'r' = \(\frac{9}{3} =\frac{27}{3} =\frac{81}{27}\)
\(= 3\)
Next term of the given geometric sequence is
\(81\) × \(3\)\(= 243\)
Hence, next term of the given sequence \(3, 9, 27, 81, . . .\)is \(243.\)
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