Question 1062804
<font color=black size=3>Looking at the denominators (3, 9, 27, 81, ...) they are powers of 3


3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
and so on...


The terms are almost of the form 1/(3^n) where n is a positive whole number starting at n = 1.  However, notice that the terms alternate in sign. This means we need to have (-1)^n in there to have the terms alternate


If n = 1, then (-1)^n = (-1)^1 = -1 making the first term negative like we want
If n = 2, then (-1)^n = (-1)^2 = 1 making the second term positive like we want
and so on...


Put this all together and the nth term is {{{(-1)^n*(1/(3^n))}}}</font>