Common ratio is positive, and one of the terms is positive => All terms are positive
P_{6} = P_{5} * t_{6} => If P_{6} > P_{5}, t_{6} > 1
P_{7} = P_{6} * t_{7} => If P_{6} > P_{7}, t_{7} < 1
t_{6} = t_{2} * r^{4} = 1000r^{4};
t_{7} = t_{2} * r^{5} = 1000r^{5}
1000r^{4} > 1 and 1000r^{5} < 1
< 1000 and > 1000.
= n.
n^{4} < 1000 and n^{5} > 1000, where n is a natural number
n^{4} < 1000 => n < 6
n^{5} > 1000 => n ≥ 4
n could be 4 or 5. Sum of possible values = 9
Correct Answer: 9