If a,b,c are in A.P,then are `a lambda,b lambda and c lambda` in AP?

If a^2,b^2,c^2 are in A.P., then the terms given below are also in A.P. a/(b+c),b/(c+a),c/(a+b) .

If a^2,b^2,c^2 are in A.P., then the terms given below are also in A.P. 1/(b+c),1/(c+a),1/(a+b) .

If a,b,c are in A.P.,prove that - a^3-8b^3+c^3+6abc=0

If 1/a,1/b,1/c are in A.P. then (b+c)/a,(c+a)/b,(a+b)/c are also in A.P.

If a,b,c are in G.P., show that 1/(a+b),1/(2b),1/(b+c) are in A.P.

Ifa,a-2 and 3a are in A.P., then the value of a is:

If a, b, c are in A.P. and a,b, d are in G.P., prove that a, a-b, d-c are in G.P.

If a, b, c are in A.P. then show that the terms given below are also in A.P. b + c, c + a, a + b

If 1/(a+b),1/(b+c),1/(c+a) are in A.P., then c^2,a^2,b^2 are in A.P.

If a, b, c are in A.P. then show that the terms given below are also in A.P. b + c - a, c + a - b, a+ b - c