General term of the sequence -1/2, 1, -7/8, 10/6...?

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If the last term is actually 10/16 rather than 10/6, then here is the pattern:
Rewrite the second term as 4/4.
Then the sequence is -1/2.4/4,-7/8,10/16, ...

The numerators form an arithmetic sequence 1, 4, 7, 10, ... with a common difference of 3. The general term for the numerators can be found using the formula a+(n-1)(d) where a is the first term.
So for the numerators, the general term is
1+(n-1)(3)
=1+3n-3
=3n-2

The denominators form a geometric sequence -2, 4, -8, 16, ...with common ratio r =-2.
The general term of a geometric sequence can be found using the formula ar^(n-1).
So for the denominators, the general term is
(-2)(-2^(n-1))

Putting this together, the general term for your sequence is
(3n-2)/(-2)(-2^(n-1))...Show more