Question

Assertion :Let a, b, c be three positive real numbers which are in H.P.

If $a,b,c$ are in A.P. and $b,c,a$ are in G.P., then $c,a,b$ are in H.P.

Reason: If $a,b,c$ are in A.P. and $b,c,a$ are in G.P. than $a:b:c=4:2:-1$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

$a+c=2b$,

also $ab=c^2$....(because $b,c,a$ are in G.P.)
Now $\frac{2bc}{b+c}=\frac{c(a+c)}{b+c}=\frac{ac+ab}{b+c}=a$
$\therefore c,a,b$ are in H.P.

However, the statement $a:b:c=4:2:-1$ is not true.