Question

The general term for the sequence 3,9,27,81,243, .... is

Answer 1

`a_n=3(3)^(n-1)`

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:

`(9)/(3) = 3\\\\(27)/(9) = 3\\\\(81)/(27) = 3`

then the radius of convergence of the series is r.

therefore this is a geometrical series.

The formula to find the general term
`a_n` of the geometric sequence is:

`a_n=a_1(r)^(n-1)`

Where

`a_1` is the first term of the sequence

Then the general term for this sequence is:

`a_n=3(3)^(n-1)`