Question

Assertion :8, 12, 18 are in $GP$, then 20, 24. 30 are in $HP$ Reason: If middle term of $GP$ is added in three consecutive terms of a $GP,$then resulting terms will be in $HP$

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

If $a,b,c\in G.P$ then $a+b,2b,c+b$ are in $H.P$.
$\Rightarrow 2b=\frac{2(a+b)(c+b)}{(a+b)+(c+b)}$ $[\because A,B,CareinHPthenB=\frac{2AC}{A+C}]$

$\Rightarrow b(a+2b+c)=(a+b)(c+b)$
$\Rightarrow ab+2b^2+bc=ac+bc+ab+b^2$
$\Rightarrow b^2=ac$
$\therefore$ Assertion (A) is true followed by Reason (R)
Ans: A