Question

If a₁, a₂, a₃,……are in G.P., then the value of

$\left| \begin{matrix} \log a_{n} & \log a_{n + 1} & \log a_{n + 2} \\ \log a_{n + 3} & \log a_{n + 4} & \log a_{n + 5} \\ \log a_{n + 6} & \log a_{n + 7} & \log a_{n + 8} \end{matrix} \right|$is –

• A. 0
• B. log (a_n a_n+8) – 2 log a_n+4
• C. log a₁ a₃ – 2 log a₂
• D. –1

Answer 1

Answer: (A)

0

Answer 2

a₁, a₂, a₃, …. are in G.P.

\ log a₁, log a₂, log a₃,…..are in A.P.

log a_n, log a_n+1, log a_n+2 are in A.P.

\ log a_n + log a_n+2 = 2 log a_n+1

Similarly, log a_n+3 + log a_n+5 = 2 log a_n+4

and log a_n+6 + log a_n+8 = 2 log a_n+7

\ Operating C₂ ® C₂ – $\frac{1}{2}$ (C₁ + C₃), the given determinant in equal to$\left| \begin{matrix} \log a_{n} & 0 & \log a_{n + 2} \\ \log a_{n + 3} & 0 & \log a_{n + 5} \\ \log a_{n + 6} & 0 & \log a_{n + 8} \end{matrix} \right|$= 0