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Question

If a,b,care in A.P., then2ax+1,2bx+1,2cx+1,x0 are in


A

A.P

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B

G.P only when x>0

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C

G.P if x<0

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D

G.P for all x0

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Solution

The correct option is D

G.P for all x0


Solving the series in AP:

Given a,b,care in AP ,

So,

2b=a+c(2bx+1)2=(22bx+2)=2(a+c)x+2=2ax+1×2cx+1

Therefore,2ax+1,2bx+1,2cx+1 are in G.P

Hence, the terms 2ax+1,2bx+1,2cx+1,x0 are in G.Pso, option (D) is correct.


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