Find the number of 6-term strictly increasing geometric progressions, such that all terms are positive integers less than 1000.
+9519 Let a = first term, r = common ratio.
Strictly increasing <-> r > 1
positive integers <-> a > 0
all terms are less than 1000 <-> ar5 < 1000
Under these three constraints, the possible pair of (a, r) are:
(1, 2), (1, 3), (2, 2), (2, 3), (3, 2), (3, 3), (4, 2), (4, 3), (5, 2)
So the required answer is 9
