Geometric Sequences

[Peter G]

I have to find the sum of a sequence. They don't tell me until what term but they give me the term itself in the sequence, so:

1/3 - 1/9 + 1/27 ..... -1/729

So I did: -1/729 = 1/3 x -1/3 ^ (n-1)
And got: n = 6

Then: Sn = 1/3 (1 + 1/3 ^ 6) / (1 + 1/3)

I get 365/1458 which is slightly different from what I get when I right all down and perform it "manually" (364/1458, thus, 182/729) and very different from the answer both in the book and what I got from a Geometric Sequence calculator online. Can anyone please help me?

Thanks