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

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 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 (a+2b-c) (2b+c-a) (c+a-b) = 4abc .

If a,b,c are in AP, show that (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab) , are also in AP.

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 (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.

if a,b,c are in AP, show that [(b+c)^(2) -a^(2)],[(c+a)^(2) -b^(2)],[(a+b)^(2) =c^(2)] are in AP.