Formula for nth Term in a Sequence: -3/2, -1/6, 1/12, 3/20, 5/30,...

kyle1

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Aug 24, 2017
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I am working on some calculus homework and need some tips on how to find the formula for the nth term in a sequence. I have been able to complete most of my homework problems using a 'guess and check' type method when finding the formulas, but there is one that is giving me a lot of trouble.
The sequence is:
{-3/2, -1/6, 1/12, 3/20, 5/30 ...}

As far as my own work goes I have noticed:
-3/2 + 4/3 = - 1/6
-1/6 + 1/4 = 1/12
1/12 + 1/15 = 3/20
3/20 + 1/60 = 5/30

But I can't find a pattern there. Any help is appreciated.
 
Consider the sequence of numerators separate from the sequence of denominators.

For the denominators, think about the squares of the Natural numbers. How do the denominators differ from the sequence of squares?
 
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