If a, b, c are in A.P., show that `2(a-b)=(a-c)=2(b-c)`

If a,b,c are in A.P., show that (a-c)^(2)=4(b^(2)-ac) .

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

If a, b, c are in A.P. then show that 2b = a + c.

If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4abc

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

If a, b, c are in A.P., show that: (b + c), (c + a) and (a + b) are also in A.P.

If a,b,c are in A.P., then show that (i) a^2(b+c), b^2(c+a), c^2(a+b) are also in A.P.

If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2)(a+b) are in A.P. (ab+bc+ca != 0)

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

If a^(2), b^(2), c^(2) are in A.P., show that, (b+c), (c+a), (a+b) are in H.P.