Let `2,A_(1),A_(2),14` are in A.P.and `2,H_(1),H_(2),14` are in H.P.,then the value of `(H_(1)+H_(2))/(A_(1)+A_(2))` is

If a,A_(1),A_(2),b are in A.P., a,G_(1),G_(2),b are in G.P. and a, H_(1),H_(2),b are in H.P., then the value of G_(1)G_(2)(H_(1)+H_(2))-H_(1)H_(2)(A_(1)+A_(2)) is

Let a_(1),a_(2),a_(3)... be in A.P.and a_(p),a_(q),a_(r) be in G.P.then value of (a_(q))/(a_(p)) is

Let f(x)=(a^(2)+b^(2)-4a-6b+13)(2x^(2)-4x+5),a,b in R such that f(0)=f(1)=f(2). If a,A_(1),A_(2),...A_(10),b is an A.P.and a,H_(1),H_(2)....H_(10),b is a H.P.then find the value of (1)/(10)(sum_(r=4)^(8)A_(r)H_(11-r))

If A_(1),A_(2),G_(1),G_(2) and H_(1),H_(2) be two AMs,GMs and HMs between two quantities then the value of (G_(1)G_(2))/(H_(1)H_(2)) is

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let /_\=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then

If A_(1),A_(2) are between two numbers, then (A_(1)+A_(2))/(H_(1)+H_(2)) is equal to

If a_(1),a_(2),...a_(n) are in H.P then the expression a_(1)a_(2)+a_(2)a_(3)+...+a_(n-1)a_(n) is equal to