SOLUTION: how to find the nth term of the following sequence. 1, -2, 3, -4, 5,...

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Question 966131: how to find the nth term of the following sequence.
1, -2, 3, -4, 5,...
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Index____________Term
1________________1
2________________1+(n-1)
3________________1+(n-1)
4________________1+(n-1)
That much helps understand the absolute values of the terms,
but the given sequence ALTERNATES in sign.



Index____________Term
1________________1%2A%28-1%29%5E%28n%2B1%29------forces sign to be positive; n+1=1+1=2.
2________________1+(n-1)
3________________1+(n-1)
4________________1+(n-1)


EACH term will use the same formula:
Index_______________Term
1__________________%281%2B%28n-1%29%29%28-1%29%5E%28n%2B1%29
2___________________%281%2B%28n-1%29%29%28-1%29%5E%28n%2B1%29


highlight%28%281%2B%28n-1%29%29%28-1%29%5E%28n%2B1%29%29, still from the point of view of a simple arithmetic sequence altered to alternate in sign. This can really be made simpler:

highlight%28highlight_green%28n%2A%28-1%29%5E%28n%2B1%29%29%29