If `a^2,b^2,c^2` are in `A. P.,` then show that `b+ c, c+a, a + b` are in `H. P.`

If a, b, c are in A.P. then show that 2b = a + c.

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

If a, b, c are in G.P. then show that b^(2 ) = a.c.

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.

(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.then prove that tan A,tan B,tan C are in H.P.

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

If a^(2),b^(2),c^(2) are in A.P.then show that: bc-a^(2),ca-b^(2),ab-c^(2) are in A.P.

If, in a /_\ABC , it is given that a^(2), b^(2), c^(2) are in an A.P., show that tan A, tan B, tan C are in the H.P.