If a, b, c are in A.P.; b, c, d are in G.P. and 1c,1d,1e are in A.P. prove that a, c, e are in G.P.
a, b, c are in A.P.
∵ b, c, d are in G.P.
Also, 1c, 1d, 1e are in A.P.
Putting value of equation (1) and (3) in (2)
which shows that a, c, e are in G.P.