If `a , b , c ,` are in `A P ,a^2,b^2,c^2` are in HP, then prove that either `a=b=c` or `a , b ,-c/2` from a GP (2003, 4M)

If a,b,c, are in AP,quad a^(2),b^(2),c^(2) are in HP ,then prove that either a=b=c or a,b,-(c)/(2) from a GP (2003,4M)

If A=2B, then prove that either c=b or a^(2)=b(c+b)

If a,b,c are in GP, a-b,c-a,b-c are in HP, then a+4b+c is equal to

If a,b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P. then prove that either a^(2),b^(2),c^(2) are in H.P.a=b=c or a,b,-(c)/(2) form a G.P.

If a, b, c are in GP, prove that a^(2), b^(2), c^(2) are in GP.

if a,b,c are in AP and b,c,a are in GP then show that c,a,b are in HP

If a,b,c are in GP,a-b,c-a,b-c are in HP. then the value of a+4b+c is

If a, b, c are in AP or GP ot HP where a>0, b>0, c>0 then prove that b^2> or = or < ac .