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`

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 a, b, c are in A.P. then show that the terms given below are also in A.P. 1/(bc),1/(ca),1/(ab)

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

If a, b, c are in A.P. then show that the terms given below are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b),{ab+bc+cane0} .

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

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. and also in GP., show that a = b = c.

If a,b,c,d are in G.P show that each of the following three term are also in G.P a+b,b+c,c+d .

If a, b, c, d are in G.P., show that each of the following three term are also in G.P. a+b,b+c,c+d .