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`

If a,b,c are in AP , show that (a+2b-c) (2b+c-a) (c+a-b) = 4abc .

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

If a+b=c , show that a^(3)+b^(3)+3abc=c^(3)

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.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 AP, show that (i) (b+c) , (c+a) and (a +b) are in AP. (ii) a^(2) (b+c) , b^(2) (c +a) and c^(2) ( a+b) are in AP.

(i) a , b, c are in H.P. , show that (b + a)/(b -a) + (b + c)/(b - c) = 2 (ii) If a^(2), b^(2), c^(2) are A.P. then b + c , c + a , a + b are in H.P. .

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

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)