Show that the sequence `(a+b)^2 (a^2+b^2), (a-b)^2, …` is an A.P.

Show that the sequence (p + q)^(2), (p^(2) + q^(2)), (p-q)^(2) … is an A.P.

Show that (a-b)^(2),(a^(2)+b^(2)) and (a+b)^(2) are in A.P.

Show that (a-b)^(2),(a^(2)+b^(2)) and (a+b)^(2) are in A.P.

Show that (a - b)^(2), (a^(2) + b^(2)) " and " (a + b)^(2) are in AP.

Show that the sequence log a,log((a^(2))/(b)),log((a^(3))/(b^(2))),log((a^(4))/(b^(3))) forms an 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, 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.

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

If a,b,c are in Ap, show that (i) (b +c-a),(c+a-b) ,(a+b-c) are in AP. (bc -a^(2)) , (ca - b^(2)), (ab -c^(2)) are in AP.

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.