If a,b , c are in AP, then, find the value of (a-c)^2/(b^2-ac)

If a ,b ,c ,and d are in H.P., then find the value of (a^(-2)-d^-2)/(b^(-2)-c^-2) .

If a, b, c are in G.P. and b-c, c-a, a-b are in H.P. then find the value of ((a+b+c)^(2))/(b^(2)) .

If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

A triangle ABC is such that sin(2A+B) =1/2 and If A, B and C are in A.P., then find the value of A and C

If [a b c]=2 , then find the value of [(a+2b-c)(a-b)(a-b-c)] .

If a ,b ,c are in A.P., then prove that: (a – c)^2 = 4(b^2 – ac).

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is (a) (ab^(2))/((2a-b)^(2)) (b) (a^(2)b)/((2a-b)^(2)) (c) (a^(2)b^(2))/((2a-b)^(2)) (d) None of these

If a, b, c are in AP, then (a - c)^(2) equals

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

If a, b, c are in A.P., then prove that : (i) ab+bc=2b^(2) (ii) (a-c)^(2)=4(b^(2)-ac) (iii) a^(2)+c^(2)+4ca=2(ab+bc+ca).