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 2b = a + c.

If a, b, c are in A.P., prove that 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., prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" are also in A.P."

If ab+bc+ca!=0 and a,b,c are in A.P. prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b) are also in A.P.

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

In triangle ABC , if cotA, cotB, cotC are in A.P. then show that a^2,b^2,c^2 are also in A.P

If a, b, c are in A.P., then show that (i) b + c – a, c + a – b, a + 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 (b^(2)+c^(2)-a^(2))/(2bc), (c^(2)+a^(2)-b^(2))/(2ca) and (a^(2)+b^(2)-c^(2))/(2ab) are in A.P. then show that, a(b+c-a), b(c+a-c) and c(a+b-c) are also in A.P. [a+b+c != 0] .