sequenc

If A₁,A₂,........A_n are n arithmetic means between a and b , a,A₁,A₂....,A_n,b ARE IN A.P.
A₁=(a + b-a/n+1) ,A₂=(a + 2(b-a)/n+1)
A_n=(a + n(b-a)/n+1)
now, A₁+A_n=A₂+A_n-1=.......=a+b(try adding them)

http://targetiit.com/iit_jee_forum/posts/hp_2_9320.html

that should help u

Since a,b,c,d are in H.P., 1/a,1/b,1/c,1/d are in A.P. 1/b - 1/a=1/c - 1/b=1/d -1/c=m then, a-b=mab ,b-c=mbc ,c-d=mcd ,1/d-1/a=3m a-d=3mad \Rightarrowa-d=m(ab+bc+cd) \Rightarrow3mad=m(ab+bc+cd)