How do I find a geometric sequence with 1 term (not the first) and the common ratio?

The nth term (for any natural number n) is

a_1 r^(n-1)

That is, it's the first term, multiplied by the (n-1)th power of the common ratio.

Reading one of your examples by twisting my head (since you posted it sideways), I see we have

a_9 = 8 and r = 1/2, so

8 = a_1 (1/2)^7

8 = a_1 (1/128)

a_1 = 8 * 128 = 1024

But I notice that what we're actually looking for here is the 10th term,

which of course is just the product of the 9th term and the ratio:

a_10 = a_9 r = 8 (1/2) = 4

For the next one, I'll just point out that since the 11th term is the product of the 10th term and the ratio, you can just DIVIDE the 11th term by the ratio to get the 10th term.