Answer:
[tex]a_n=3(3)^{n-1}[/tex]
Step-by-step explanation:
We have the following sequence
3,9,27,81,243
Note that if you divide each term of the sequence between the previous term you get:
[tex]\frac{9}{3} = 3\\\\\frac{27}{9} = 3\\\\\frac{81}{27} = 3[/tex]
then the radius of convergence of the series is r.
therefore this is a geometrical series.
The formula to find the general term [tex]a_n[/tex] of the geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where
[tex]a_1[/tex] is the first term of the sequence
Then the general term for this sequence is:
[tex]a_n=3(3)^{n-1}[/tex]
