Let `a_1, a_2, a_3, ,a_(100)` be an arithmetic progression with `a_1=3a n ds_p=sum_(i=1)^p a_i ,1lt=plt=100.` For any integer `n` with `1lt=nlt=20 ,` let`m=5ndot` If `(S_m)/(S_n)` does not depend on `n ,` then `a_2` is__________.

Options

A. 9
B. 8
C. 7
D. 5

Answer

A

Explanation

Since `a_(1),a_(2),a_(3), . . . .,a_(100)` is an A.P. with `a_(1)=3andS_(p)=underset(i=1)overset(p)suma_(i)`.
`:." "(S_(m))/(S_(n))=(S_(5n))/(S_(n))=((5n)/(2){2xx3+(5n-1)xxd})/((n)/(2){2xx3+(n-1)xxd})=(5(5nd+6-d))/((nd+6-d))`
Clearly, it will be independent of n if 6-d=0 i.e. d=6.
`:." "a_(2)=a_(1)+d=3+6=9`