Problem Solving of AP,GP,HP,AGP

AP ||GP

If x y z are in GP(x y z>1) then (1)/(2x+log x) , (1)/(4x+log y) , (1)/(6x+log z) are in 1) AP 2) GP 3) HP 4) AGP

Let the positive numebrs a,b,c,d be in A.P. Then abc,abd,acd,bcd re (A) not in A.P., G.P., H.P. (B) in A.P. (C) in G.P. (D) in H.P.

Intro Ap,GP,HP,Pro Summation of Series GP,AM-GM Inequality

If x, y ,z are in AP, then (1)/(sqrtx+sqrty) , (1)/(sqrtz+ sqrtx), (1)/(sqrty+sqrtz) are in: a)AP b)GP c)HP d)AP and HP

If three positive numbers a,b and c are in AP, GP and HP as well, than find their values.

If three positive numbers a,b and c are in AP, GP and HP as well, than find their values.

If three positive numbers a,b and c are in AP, GP and HP as well, than find their values.

Prove that, a, b,c are in A.P., G.P. or, H.P. accordingly as (a-b)/(b-c) = 1 or (a)/(b) or, (a)/(c ) .

If three positive numbers a,b and c are in AP, GP and HP as well, than find their values.