If a, b, c are in A.P., prove that `a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).`

If a,b,c, are in AP, prove that a^(3) + 4b^(3)+c^(3)= 3b (a^(2)+c^(2))

If a,b,c are in A.P.,prove that 8b^(3)-a^(3)-c^(3)=3ac(a+c)

If a,b,c are in A.P. prove that (a-c)^(2)=4(a-b)(b-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)+c^(2)-2bc=2a(b-c) .

If a,b,c are in G.P.,prove that: a(b^(2)+c^(2))=c(a^(2)+b^(2))A^(2)b^(2)c^(2)((1)/(a^(3))+(1)/(b^(3))+(1)/(c^(3)))=a^(3)+b^(3)+c^(3)((a+b+c)^(2))/(a^(2)+b^(2)+c^(2))=(a+b+c)/(a-b+c)(1)/(a^(2)-b^(2))+(1)/(b^(2))=(1)/(b^(2)-c^(2))(a+2b=2c)(a-2b+2c)=a^(2)+4c^(2)

If a,b,c are in A.P.,prove that: (a-c)^(2)=4(a-b)(b-c)a^(2)+c^(2)+4ac=2(ab+bc+ca)a^(3)+c^(3)+6abc=8b^(3)

If a,b,c are in A.P.then prove that: (a-c)^(2)=4(b^(2)-ac)a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2))

If a,b,c are in A.P,show that (i)a^(3)+b^(3)+6abc=8b^(3)( ii) (a+2b-c)(2b+c-a)(a+c-b)=4abc