Question

If $a_n(>0)$ be the $n^{\text{th }}$ term of a G.P. then
$\left|\begin{array}{ccc}\log a_n& \log a_{n+1}& \log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}& \log a_{n+5}\\ \log a_{n+6}& \log a_{n+7}& \log a_{n+8}\end{array}\right|$ is equal to

• A. 1
• B. 2
• C. -2
• D. 0

Answer 1

Answer: (D)

$\therefore \left|\begin{array}{ccc}\log a+(n-1)\log r& \log a+n\log r& \log a+(n+1)\log r\\ \log a+(n+2)\log r& \log a+(n+3)\log r& \log a+(n+4)\log r\\ \log a+(n+5)\log r& \log a+(n+6)\log r& \log a+(n+7)\log r\end{array}\right|$
$R_2\to R_2-R_1,R_3\to R_3-R_1$
$\therefore \left|\begin{array}{ccc}\log a+(n-1)\log r& \log a+n\log r& \log a+(n+1)\log r\\ 3\log r& 3\log r& 3\log r\\ 6\log r& 6\log r& 6\log r\end{array}\right|$
$=0$