Question 1062804: find the nth term of this sequence:
-1/3,1/9,-1/27,1/81,.....
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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 
Answer by Edwin McCravy(20054)  (Show Source):
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