What is the 10th term in the following sequence. 7/9, 7/3, 7, -21, 63. Help?!?!?!?

You have an ERROR in your post...either (- 21) is incorrect or the second term should be (- 7/3)...

Correct your post !

The nth term could be (203/27)n^4 - (2191/27)n^3 + (8113/27)n^2 - (12005/27)n + (1967/9)
In that case, the 10th term is 178717/9

Note: This can NOT be an arithmetic or geometric sequence.

This looks like a geometric sequence

with first term 7/9 and common ratio 3

- except for - 21. Are you sure all the signs are right?

It looks like your geometric sequence has a common ratio of 3. The 10th term will be
.. (7/9)*3^9 = 15,309
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Assuming the 4th term is 21, not -21.

-189......only I think you have a typo. I suspect that 63 is really -63. If it isn't I'm no help. The successive term to each of the terms you've written is obtained by dividing the previous term by 1/3rd. The next should be -567.