Let a₁, a₂, a₃, ., a₁₀₀ be an arithmetic progression with a₁=3 and S_p= _ i=1 ^p a_i , 1 p 100 . For any integer n with 1 n 20 , let m=5 n . If S_m S_n does not depend on n , then a₂ is

Step-by-step solution

Given, a₁=3, m=5 n and a₁, a₂, are in AP. S_m S_n = S_ 5 n S_n is independent of n . Now, 5 n 2 [2 3+(5 n-1) d] n 2 [2 3+(n-1) d] f (6-d)+5 n (6-d)+n independent of n , if aligned 6-d= & 0 d=6 a₂= & a₁+d=3+6=9 & Or aligned If d=0 S_m S_n is independent of n . a₂=3