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Grade: 11
        
3 non zero number a,b, and c are in AP increasing a by 1 or increasing or c by 2 the numbers are in GP then b equal
8 months ago

Answers : (1)

Devang
52 Points
							
a,b,c are in A.P.
Then 
   a+c = 2b.            .......(1)
Increasing a by 1 (a+1),b,c are in G.P.
Then
  (a+1)(c) = b^2.   .......(2)
Increasing c by 2 a,b,(c+2) are in G.P. 
Then
   (a)(c+2)=b^2.   .........(3)
From (2) & (3)
ac + c = ac + 2a
   c = 2a.       .........(4)
Put c = 2a in eq. (1)
Then
3a = 2b
b= 3a/2.        .....(5)
Put value of (4) & (5) in (2)
(3a/2)^2 = (a+1) (2a)
Solving this eq. We get a = 8.   
Put a= 8 in (5)
We get,
                        b=12
 
8 months ago
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