Let `a_1,a_2,a_3,……,a100` be an arithmetic progression with `a_1=3 and S_p=Sigma_(i=1)^(p) a_i, 1 le p le 100`. For any integer n with `1 le n le 20 , let m=5 n`. If `(S_m)/(S_n)` does not depend on .n then `a_2` is _________.

Answer

6

Explanation

`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