Here we can see the numerator is decreasing by one in each subsequent part of the series (-1,-2,-3,-4,etc)

The denominator is increasing by 3 each time, meaning that the denominator has 3n as part of its function. By substituting in one of the examples, we see that the denominator is 3n-2

The general formula for the nth term is then -n/(3n-2)

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Andrew Bradshaw
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