CAT Progressions

Question
Second term of a GP is 1000 and the common ratio is   where n is a natural number. Pn is the product of n terms of this GP. P6 > P5 and P6 > P7, what is the sum of all possible values of n?
A.            5
B.            9
C.            8
D.            11
Correct Answer
Choice B
Explanatory Answer
Common ratio is positive, and one of the terms is positive => All terms are positive
P6 = P5 * t6=> If P6 > P5, t6 > 1
P7 = P6 * t7=> If P6 > P7, t7 < 1
T6 = t2* r4 = 1000r4;
T7 = t2* r5 = 1000r5
1000r4> 1 and 1000r5 < 1
1/r^4 < 1000 and 1/r^5 > 1000
1/r = n
n4 < 1000 and n5> 1000, where n is a natural number
n4 < 1000 => n < 6
n5 > 1000 => n > 4
n could be 4 or 5. Sum of possible values = 9
Answer Choice (B)

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