Question

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

Answer 1

whats your progress so far ?

Answer 2

i have to solve it back wards......

Answer 3

yep..
you'll have to prove
(a-b)(c-d)=(b-c)^2

using ac=b^2

Answer 4

and ad=c^2 ,also ad=bc

Answer 5

correction: bd=c^2

Answer 6

its upside down,,please re-adjust..

Answer 7

anyways,,i could read it,,and you'll done right till now..i'll write the last step here
b^2 + c^2 -2bc = ac+bd-bc-ad

Answer 8

you have to prove LHS = RHS
start with any, say LHS

Answer 9

substitute b^2 = ac
c^2 = bd

Answer 10

also we know bc=ad
so 2bc = bc + ad

make these substitutions and there it is..