If `a ,b ,c` are in G.P. and `a-b ,c-a ,a n db-c` are in H.P., then prove that `a+4b+c` is equal to 0.

If a,b,c are in G.P.and a-b,c-a, and b-c are in H.P.then prove that a+4b+c is equal to 0.

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. and a^2, b^2, c^2 are in H.P., then prove that either a=b=cora ,b ,-c/2 form a G.P.

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c+c/a

If a, b, c are in A.P. and a,b, d are in G.P., prove that a, a-b, d-c are in G.P.

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a. a/c+c/a b. a/c-c/a c. b/q + q/b d. b/q - q/b

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b