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Evaluation of a Determinant

If a 1, a 2, ...

Question

If a₁, a₂, a₃, . . . . . . , a_n . . . . . . .are in GP, then the value of the determinant

A

0

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B

1

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C

2

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D

-2

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Solution

The correct option is A
0

Let r be the common ratio of GP

∴ Given determinant,

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Similar questions

a_{1}, a_{2}, a_{3} . . . a_{n} \in G P

then the value of the determinant

△ = ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣

a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots

are in GP, then the value of the determinant

∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣

a_{1}, a_{2}, a_{3}, . . ., a_{n}, . . .

G P

then the determinant

Δ = ∣ ∣ ∣ ∣ \begin{matrix} l o g a_{n} & l o g a_{n + 1} & l o g a_{n + 2} l o g a_{n + 3} & l o g a_{n + 4} & l o g a_{n + 5} l o g a_{n + 6} & l o g a_{n + 7} & l o g a_{n + 8} \end{matrix} ∣ ∣ ∣ ∣

a_{1}, a_{2}, a_{3}, . . . . .

are in G.P. then the value of determinant

∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣

a_{1}, a_{2}, a_{3}, . . . a_{n,} . . .

are in G.P., then the determinant

Δ = ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣

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