One way to solve it is to notice that to get from 2187 to 729 you have to divide
2187 by 3.  And to get 729 to 243 you must also divide by 3.  So you can get the
answer by asking this question:

If I start with 2187, how many times must I divide by 3 until I get 1/9?

Then the answer will be one more than that because the first time I divide
will be to get the second term. 



Cross multiplying











So it's 1 more than 9, so it's the 10th term.

That's not how you're supposed to do it, though.

You're supposed to use geometric series formula, like that baby in the
picture up there did it.



with , , 

and solve for n.  You can use logs to solve it if you like.

Edwin