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: i. (a-c)^2=4(a-b)(b-c) ii. a^2+c^2+4a c=2(a b+b c+c a) iii. a^3+c^3+6a b c=8b^3

If a, b, c are in A.P., prove that : (a(b+c))/(bc), (b(c+a))/ (ca), (c(a+b))/(ab) are also in A.P.

Suppose a, b, c are in A.P. Prove that (a+2b-c)(2b+c-a)(c+a-b)=4abc

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 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 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 is the smallest side of a triangle and a,b,c are in A.P. prove that "cos" A=(4c-3b)/(2c)

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. and a, b, c + 1 are in G.P. then prove that 4a=(a-c)^2 .

If a ,b ,c are in A.P., prove that 1/(b c),1/(c a),1/(a b), is also in A.P.