Let `a_n` be the nth term of a G.P. of positive numbers. Let `sum_(n=1)^(100)a_(2n)=alpha` and `sum_(n=1)^(100)a_(2n-1)=beta` , such that `alpha!=beta` , then the common ratio is `alpha//beta` b. `beta//alpha` c. `sqrt(alpha//beta)` d. `sqrt(beta//alpha)`

Answer

` r= alpha / beta`

Explanation

Let us consider,

`a` be the first term and `r` be the common ratio of the G.P.



Then,



`sum_(n=1)^(100)a_(2n)=alpha`
and `sum_(n=1)^(100)a_(2n-1)=beta`




...