Question

If a,b,c are in A.P. and a,b,(c+1) are in G.P, show that : a=(a-b)²

Answer 1

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If a,b,c are in A.P and a,x,b and b,y,c are in G.P , show that x

2

,b

2

,y

2

are in A.P.

Easy

Solution

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We have,

a,b,c are in A.P.

2b=a+c ……. (1)

a,x,b are in G.P.

x

2

=ab …… (2)

b,y,c are in G.P.

y

2

=bc ……. (3)

From equation (1) and (2), we get

x

2

=(2b−c)b

x

2

=2b

2

−bc

On putting the value of bc in above expression, we get

x

2

=2b

2

−y

2

2b

2

=x

2

+y

2

So, x

2

,b

2

,y

2

are in A.P.

Hence, proved.