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Question

If a,b and c are in AP, then which one of the following is not true?


A

ka,kb,kc are in HP

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B

a+k,b+k,c+k are in AP

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C

ka,kb,kc are in AP

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D

a2,b2,c2 are in AP

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Solution

The correct option is D

a2,b2,c2 are in AP


Explanation for the correct option:

Given, a,b,c are in AP

For this we will check the option D.

If a2,b2,c2 are in AP, then

b2-a2=c2-b2

(b-a)(b+a)=(c-b)(c+a)

common difference of an A.P is always constant

b-a=c-b

b+b=a+c

2b=a+c

b+a=c+a is not possible.

So this Option is false.

Hence, option ‘D’ is Correct.


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