Determinants Matrices Question 145
Question: If $ a_1,a_2,a_3,………… $ are positive numbers in G.P. then the value of $ \begin{vmatrix} \log a _{n} & \log {a _{n+1}} & \log {a _{n+2}} \\ \log {a _{n+1}} & \log {a _{n+2}} & {loga _{n+3}} \\ \log {a _{n+2}} & \log {a _{n+3}} & \log {a _{n+4}} \\ \end{vmatrix} $
Options:
A) $ 1 $
B) $ 4 $
C) $ 3 $
D) $ 0 $
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Answer:
Correct Answer: D
Solution:
- [d] If the G.P be $ a,ar,ar^{2},…. $ then $ a _{n}=a{r^{n-1}} $
$ R_3\to R_3-R_2 $ and $ R_2\to R_2-R_1 $ gives, $ = \begin{vmatrix} \log a+(n-1)logr & \log a+n\log r & \log a+(n+1)logr \\ \log r & lorr & \log r \\ \log r & \log r & \log r \\ \end{vmatrix} $
= 0, since $ R_2 $ and $ R_3 $ are identical.
BETA
