Question

Second term of a GP is 1000 and the common ratio is r = 1n 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

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

CORRECT ANSWER WRONG ANSWER

Solution

Correct option is

(B)

Explanatory Answer

according to ques , common ratio is positive and one term is positive which means = all terms should be positive.

$p_{6} =p _{5} *t_{6} = if p_{6}>p_{5} , t_{6}> 1$

$p_{7} =p _{6} *t_{7} = if p_{6}>p_{7} , t_{7}< 1$

$t_{6} =t _{2} *r^{4} = 1000 r^{4}$

$t_{7} =t _{2} *r^{5} = 1000 r^{5}$

$1000 r^{4} >1 and 1000 r^{5} < 1$

$1/r^{4} < 1000 ;and ; 1/ r^{5} > 1 000$

1/r = n

$n^{4} < 1000 => n< 6 ;and ; n^{5} > 1000 => n geq 4$

n can be 4 or 5 , sum of possible values = 9

so , B is the correct option