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)\[-2\]
Correct Answer:
A
Solution :
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)