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