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

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 ,d are in G.P., prove that a+b,b+c ,c+d are also in G.P.

If a, b, c are in G.P. and also a, b, c are in A.P. Prove that: 1/a+1/c=2/b

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a, c, e are in G.P.

If a,b,c,d are in G.P.,prove that a+b,b+c,c+d are also in G.P.

If a, b, c are in A.P, b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P, b, c, d are in G.P. and 1/c , 1/d,1/e are in A. P . Prove that a, c, e are in G.P.