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)