If a,b,c are in G.P., show that `1/a,1/b,1/c` are also in G.P.

If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove that : 1/a,1/b,1/c are also in A.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2),b^(2),c^(2) .

If a, b,c are in G.P., prove that the following are also in G.P. : a^(3),b^(3),c^(3) .

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2)+b^(2),ab+bc,b^(2)+c^(2) .

If a, b, c are in A.P., prove that : b+c,c+a,a+ b are also in A.P.

If the roots of the equation : a(b - c)x^2 +b (c - a)x + c(a - b) = 0 are equal, show that 1/a,1/b,1/c are in A.P.

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

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

If a, b,c are in G.P, then log a, log b, log c are: