Can you see the pattern? The signs are alternating, the numerator is just counting, and the denominator is of the form 3n. We could just continue the pattern for a few more terms, or recognize that each term can be represented by:
A(n)=(-1)n(n/3n)
That first part, with the -1 will just allow the terms to alternate in sign. Look at the second term of 2/9. If we plug 2 in for n, we get (-1)2(2/32), or 2/9, so it appears to work.
A(9)=(-1)9(9/39) = -9/19,683, which can be simplified to -1/2187, but I would probably leave it in the first form, to match the other terms.
