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Find the number of 6-term strictly increasing geometric progressions, such that all terms are positive integers less than 1000.

 Jun 15, 2020
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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

 Jun 15, 2020

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