Question

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

• A. $\frac{k}{a},\frac{k}{b},\frac{k}{c}$ are in HP
• B. $a+k,b+k,c+k$ are in AP
• C. $ka,kb,kc$ are in AP
• D. $a^2,b^2,c^2$ are in AP

Answer 1

The correct option is D

$a^2,b^2,c^2$ are in AP

Explanation for the correct option:

Given, $a,b,c$ are in AP

For this we will check the option D.

If $a^2,b^2,c^2$ are in AP, then

$b^2-a^2=c^2-b^2$

$\Rightarrow$$(b-a)(b+a)=(c-b)(c+a)$

$\because$common difference of an A.P is always constant

$\Rightarrow$ $b-a=c-b$

$\Rightarrow$$b+b=a+c$

$\Rightarrow$ $2b=a+c$

$\therefore b+a=c+a$ is not possible.

So this Option is false.

Hence, option ‘D’ is Correct.