A) \[3\]
B) \[2\]
C) \[1\]
D) \[zero\]
Correct Answer: D
Solution :
Let the first term and common ratio of a \[GP\] be \[A\] and R\[R\] respectively. \[l=A{{R}^{p-1}}\Rightarrow \log l=A+(p-1)\log R\] \[m=A{{R}^{q-1}}\Rightarrow \log m=\log A+(q-1)\log R\] \[n=A{{R}^{r-1}}\Rightarrow \log n=A+(r-1)\log R\] Now, \[\left| \begin{matrix} \log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1 \\ \end{matrix} \right|\] \[=\left| \begin{matrix} \log A+(p-1) & \log R & p\,\,\,1 \\ \log A+(q-1) & \log R & q\,\,\,1 \\ \log A+(r=1) & \log R & r\,\,\,1 \\ \end{matrix} \right|=0\]You need to login to perform this action.
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