Mathematics - Determinant Question with Solution | TestHub

$$\begin{array}{rl}& \left|\begin{array}{lll}\log a_n& \log a_{n+1}& \log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}& \log a_{n+5}\\ \log a_{n+6}& \log a_{n+7}& \log a_{n+8}\end{array}\right|\\ & C_3\to C_3-C_2,C_2\to C_3-C_1\\ & =\left|\begin{array}{lll}\log a_n& \log r& \log r\\ \log a_{n+3}& \log r& \log r\\ \log a_{n+6}& \log r& \log r\end{array}\right|=0\end{array}$$ (where $r$ is a common ratio).