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Let a1, a2, a3, ,a(100) be an arithmeti...

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__________.

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The correct Answer is:
6
`a_1,a_2,a_3,.....,a_100` is an A.P
`a_1+3,S_p=underset(i=1)overset(p)Sigma a_a,1 le p le 100`
`(S_m)/(S_(n))=(S_(5n))/(S_n)=((5n)/(2)(6+(5n-1)d))/(n/2(6+(n-1)d))`
`S_m/S_n` is independent of n of 6-d =0 `rArr` d=6
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