If a,b,c are in A.P and a,b,din G.P., then a,a-b,d-c will be in
A.P
G.P
H.P
None of these
Step 1. Finding the progression:
Given that, a,b,c are in AP and a,b,din GP
Then, 2b=a+c...(i)
∵a,b,din GP
∴b2=ad(ii)
Step 2. Multiply equation (i) by 'a'
2ab=a2+ac
⇒ -ac=a2-2ab
Step 3. Add b2on both side,
b2-ac=a2-2ab+b2
⇒ ad-ac=(a-b)2 ; [∴b2=ad]
⇒ a(d-c)=(a-b)2
∴a,(a-b),(d-c) are in GP
Hence, correct option is (B).