Question 1194672: Find the nth term for sequence
-1/27, 1/3, -5/3, 7
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Technically, the question can't be answered, because any next number(s) would form a valid sequence, and obviously different subsequent numbers would require different forms of the formula for the n-th term.
But in this example it is fairly clear what the intended sequence is.
To see the pattern and be able to write a formula for the n-th term, notice the denominators of the terms: 27, 3, 3, 1. Then rewrite the second term as an equivalent fraction with denominator 9, so that the denominators are decreasing powers of 3:
-1/27, 3/9, -5/3, 7/1
Now we have a clear pattern:
(1) alternating signs, with first term negative
To get that, we need a factor of  in the numerator
(2) numerator (ignoring the alternating signs): consecutive odd numbers starting with 1
For that, we need a factor of  in the numerator
(3) denominator: powers of 3, starting with 3 for the first term and decreasing by 1
For that, we need a factor of  in the denominator
ANSWER: 
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