• # question_answer If${{a}_{1}},{{a}_{2}},{{a}_{3}}....,{{a}_{n}},...$are in GP, then the value of the determinant $\left| \begin{matrix} \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}} \\ \log \,\,{{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}} \\ \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}} \\ \end{matrix} \right|,$ is A) 0        B)                                        1                              C) 2                              D) $-2$

Sinceare in GP. Then,    $\log \,{{a}_{n}}\,=\log \,{{a}_{1}}\,+(n-1)\,\log \,r$                                                     ??????                 ??????                 ??????                           Now,                                                 Applying,and                                                   (since, two rows are identical) Alternate Solution Since,are in GP, then are in Ap. Given that where, a and c/ are the first term and common difference of an AP. Applying  (since, two columns are identical)