Question

How do you write the expression for the nth term of the sequence given `1/3, 2/9, 4/27, 8/81,...`?

Answer 1

`a_n=2^(n-1)/3^n`

Explanation:

First look at the bottom and see how it is increasing. `3, 9, 21, 81`. Looks like for each number it increases, it is `3` to the something power, so we have `3^n`. Now we will look at the top and try and guess what causes `1, 2, 4, 8`. Look's like it is `2` to the something power, except for `1`, so it must going to the `0` power, in order for it to turn `0`. Now we have `2^(n-1)`

This is why we have: `a_n=2^(n-1)/3^n`