Question

Question #944c9

Answer 1

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

Explanation:

The given sequence `(1, - 3, 9, -27, ...)` is a geometric sequence with a common ratio of `- 3`.

The general term of any geometric sequence is in the form `a_(n) = a_(1) r^(n - 1)`; where `a_(n)` is the `n`th term, `a_(1)` is the first term, `r` is the common ratio, and `n` is the term number.

Using this information, let's form an expression for the general term of the given sequence:

`Rightarrow a_(n) = 1 cdot (- 3)^(n - 1)`

`therefore a_(n) = (- 3)^(n - 1)`

Therefore, the answer you came up with was correct.

Answer 2

`(-1)^(n-1)xx3^(n-1)`

Explanation:

The answer below or the other one was correct however I learned to do it a differenet way. I would write the negative sign in a different equation

`(-1)^(n-1)xx3^(n-1)`

I hope that helped you a little.