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

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))