Question
Question: If a, b, c are in A.P. b, c, d are in G.P. and c, d, e are in H.P. then a, c, e are always in :...
If a, b, c are in A.P. b, c, d are in G.P. and c, d, e are in H.P. then a, c, e are always in :
A
A.P
B
G.P.
C
H.P.
D
None of these
Answer
G.P.
Explanation
Solution
since a, b, c are in A.P.
\ 2b = a + c .......(i)
since b, c, d are in G.P.
\ c2 = bd ..........(ii)
since c, d, e are in H.P.
d = 
............(iii)
from (i) and (iii)
2bd = 
c2 = 
[Q bd = c2]
̃ c(c + e) = (a + c)e
̃ c2 + ec = ae + ec
̃ c2 = ae
Hence a, c, e are always in G.P.