maths question puzzle difficult?

Question

Jo is practising pool on an American 9-ball pool table, where the balls are numbered from 1 to 9. Jo picks a geometric sequence and, if there are balls on the table whose numbers are in that sequence, then Jo pots all of them. Jo keeps picking geometric sequences (and potting the corresponding balls) until all nine balls have been potted.

If Jo is very good, and never misses a shot, what is the least number of geometric sequences that Jo needs to pick in order to clear the table?

HINT: You may need to use sequences with a ratio that is a whole number or a fraction.

Answer 1

seems like I answered this yesterday:
1,2,4,8 ......... ratio 2
3,9 .............. ratio 3
5,7 ............... ratio 7/5
6
that's 4 sequences. you can't do 3,6,9 because that's arithmetic, not geometric.

Answer 2

Any set of numbers lies arbitrarily close to a geometric sequence.

For example there is a sequence containing 1, 2 and 3. The number 1 is the first term and 3 is the thousand-and-first of the geometric sequence that begins with 1 and has a constant ratio of 3^(1/1000). The 631st term of this sequence is about 2.000154 which I think Jo would feel is close enough to 2.

631/1000 is approximately log(2)/log(3)

This particular sequence has
4.0006 as the 1262nd term,
5.0001 as the 1465th term,
6.0005 as the 1631st term,
7.0058 as the 1772nd term,
8.0019 as the 1893rd term, and
9 as the 2000th term.

All close enough to a single geometric sequence.